GRK 1529:  Mathematical Fluid Dynamics

• Subject Area: Mathematics
• Term: from 2009 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 69014896

• Final Report Year: 2018

Final Report Abstract

In modern mathematical fluid dynamics, fundamental well-posedness questions for viscous and inviscid fluids as well as more applied topics such as vorticity behavior, boundary layers and free boundary value problems for Newtonian, complex as well as for geophysical fluids play a dominant role. The rigorous mathematical treatment of the underlying structures requires novel concepts and methods from various disciplines in mathematics ranging from modeling, analysis and stochastics over numerics, optimization and inverse problems up to the theory of computability and complexity. The IRTG 1529 aimed to examine the mathematical structures of the underlying equations and to apply the results to various models describing e.g. geophysical flows, fluid mixtures, hydrodynamic limits, and free or moving boundary value problems for complex fluids. Major contributions to these problems are due to the principal investigators from Waseda University, University of Tokyo and TU Darmstadt. Students with a thorough background in at least one of the fields of analysis, stochastics, modeling, complexity and computablity theory, numerics, sceintific computation or optimization received an interdisciplinary education in key areas of mathematical fluid dynamics, enabling them to successfully pursue research on problems, which without our common study program and without the cooperation with our Japanese partners would have been much more difficult or even impossible to handle. The yearlong interdisciplinary course, and later on special courses and seminars taught jointly by our German-Japanese team, provided students with one common scientific language in fluid dynamics. This broad but nevertheless focused education was needed to successfully treat our scientific projects. The research of our students was guided by an advisor and co-advisors in Darmstadt and Tokyo. Students from Darmstadt were requested to spend at least 6 months in Tokyo working there with their coadvisor. Due to this international component, the scientific visibility of the PhDs was certainly a high one. IRTG 1529 was embedded in a very active and well established research environment in Darmstadt and its counterparts in Tokyo. Our extensive conference and guest programs exposed our students to latest research results and gave them the opportunity to interact with leading experts already at an early stage of their projects. Special courses or tutorials were often embedded into workshops or conferences organized by IRTG 1529. The combiniation between tutorials and the presentation of prevailing research results within workshops was very sucessful and ensured that almost all of our doctoral students completed their PhD within 3 years. After a thesis written by an IRTG student was submitted to the Department of Mathematics at TU Darmstadt, the thesis committee needed to require at least one official report on this thesis by the Japanese co-advisor of this student. His judgement including his grade were taken into account with equal weight as the other reports. The scientific output of all projects includes in total 410 publications in refereed journals, in particular 287 publications, often in excellent journals, authored or coauthored by students or postdocs inside IRTG 1529 funded by DFG and JSPS and 73 joint German-Japanese publications, also often in excellent journals, authored or coauthored by students, postdocs or professors inside IRTG 1529 and funded by DFG or JSPS.

Publications

• Energy-based regularity criteria for the Navier-Stokes equations, J. Math. Fluid Mech., 11, (2009), 428–442
  Farwig, Reinhard; Kozono, Hideo & Sohr, Hermann
  
• Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type, J. E Equ., 8, (2008), 693–725
  Takada, Ryo
  
• On the Lp − Lq maximal regularity for the linear thermoelastic plate equation in a bounded domain, Math. Methods Appl. Sci., 32, (2009), no. 13, 1609–1637
  Naito, Yuka
  
• A continuous adjoint approach to shape optimization for Navier-Stokes flow, Optimal control of coupled systems of partial differential equations, International Series of Numerical Mathematics, Birkhäuser, 158, (2009), 35–56
  Brandenburg, Christian; Lindemann, Florian; Ulbrich, Michael & Ulbrich, Stefan
  
• Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle, Ann. Univ. Ferrera, 55, (2009), 263–277
  Farwig, Reinhard & Hishida, Toshiaki
  
• Difference approximation to Aubry-Mather sets, RIMS Kôkyûroku, Kyoto University, 1688, (2009), 7-19
  K. Soga
  
• Finite-type invariants for curves on surfaces, Proc. Japan Acad. Ser. A Math. Sci., 85, (2009), 129–134
  Ito, Noboru
  
• On the Lpp analytic semigroup associated with the linear thermoelastic plate equations in the half-space, J. Math. Soc. Japan, 61, (2009), no. 4, 971–1011
  NAITO, Yuka & SHIBATA, Yoshihiro
  
• On the Stokes operator in general unbounded domains, Hokkaido Math. J., 38, (2009), 111–136
  FARWIG, Reinhard; KOZONO, Hideo & SOHR, Hermann
  
• Periodic solutions of the forced Burgers equation, RIMS Kôkyûroku, 1631, (2009), 147–159
  T. Nishida, K. Soga
  
• Regularity of weak solutions for the Navier-Stokes system via energy criteria, In: Adv. Math. Fluid Mech., Springer, (2010), 215—227
  Farwig, Reinhard; Kozono, Hideo & Sohr, Hermann
  
• Stability of plane Couette flows with respect to small periodic perturbations, Nonlinear Anal., 71, (2009), 3739–3758
  Heck, Horst; Kim, Hyunseok & Kozono, Hideo
  
• The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework. Math. Z., 265, (2010), 481–491
  Hieber, Matthias & Shibata, Yoshihiro
  
• Uniqueness of Positive Solutions for a Nonlinear Elliptic System, NoDEA, 16, (2009), 555–567
  Ikoma, Norihisa
  
• A local mountain pass type result for a system of nonlinear Schrödinger equations, Calc. Var. Partial Differential Equations, 40, (2011), 449–480
  Ikoma, Norihisa & Tanaka, Kazunaga
  
• A point-wise criterion for quasi-periodic motions in the KAM theory, Nonlinear Analysis, 73, (2010), 3151-3161
  Soga, Kohei
  
• Asymptotic behaviors and classical limits of solutions to a quantum drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci., 20, (2010), 909–936
  NISHIBATA, SHINYA; SHIGETA, NAOTAKA & SUZUKI, MASAHIRO
  
• Construction of invariants of curves and fronts using word theory, J. Knot Theory Ramifications, 19, (2010), 1205–1245
  ITO, NOBORU
  
• Counterexamples of commutator estimates in the Besov and the Triebel-Lizorkin spaces related to the Euler equations, SIAM J. Math. Anal., 42, (2010), 2473–2483
  Takada, Ryo
  
• Existence of standing waves for coupled nonlinear Schrödinger equations, Tokyo J. Math., 33, (2010), 89–116
  IKOMA, Norihisa
  
• Global weak solutions of the Navier-Stokes system with nonzero boundary conditions, Funkcialaj Ekvacioj, 53, (2010), 231–247
  Farwig, R.; Kozono, H. & Sohr, H.
  
• Low frequency expansion in thermoelasticity with second sound in three dimensions, J. Math. Soc. Japan, 62, (2010), 1289–1316
  NAITO, Yuka; RACKE, Reinhard & SHIBATA, Yoshihiro
  
• Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class, J. Math. Anal. Appl., 365, (2010), 60–66
  Kozono, Hideo; Sugiyama, Yoshie & Takada, Ryo
  
• Nonlinear Partial Differential Equations. Progress in Nonlinear Differential Equations and their Applications, 79, Birkhauser Boston, 2010
  Giga, Mi-Ho; Giga, Yoshikazu & Saal, Jürgen
  
• Nonlinear scalar field equations in RN : mountain pass and symmetric mountain pass approaches, Topol. Methods Nonlinear Anal., 35, (2010), 253–276
  J. Hirata, N. Ikoma, K. Tanaka
  
• On quasilinear parabolic evolution equations in weighted Lp-spaces, J. Evol. Equ., 10, (2010), no. 2, 443–463
  Köhne, Matthias; Prüss, Jan & Wilke, Mathias
  
• On the energy equality of Navier-Stokes equations in general domains, Arch. Math., 95, (2010), 447–456
  Farwig, Reinhard & Taniuchi, Yasushi
  
• Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56, (2010), 249–281
  Farwig, Reinhard & Okabe, Takahiro
  
• Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56, (2010), 249–281
  Farwig, Reinhard & Okabe, Takahiro
  
• Periodic solutions of the Navier-Stokes equations with the inhomogeneous time dependent boundary data under the general flux condition, J. Evol. Equ., 11, (2011), 265–286
  Okabe, Takahiro
  
• Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differential Equations, 249, (2010), 1385–1409
  Nishibata, Shinya & Suzuki, Masahiro
  
• Remarks on the Lp-approach to the Stokes equation on unbounded domains, Discrete Contin. Dyn. Syst. Ser. S, 3, (2010), 291–297
  Geissert, Matthias; Heck, Horst; Hieber, Matthias & Sawada, Okihiro
  
• Remarks on the Lp-approach to the Stokes equation on unbounded domains, Discrete Contin. Dyn. Syst. Ser. S, 3, (2010), 291–297
  Geissert, Matthias; Heck, Horst; Hieber, Matthias & Sawada, Okihiro
  
• Steady-state Navier-Stokes flows past a rotating body: Leray solutions are physically reasonable, Arch. Ration. Mech. Anal., 200, (2011), 21–58
  Galdi, Giovanni P. & Kyed, Mads
  
• A non-autonomous model problem for the Oseen-Navier-Stokes flow with rotating effects, J. Math. Soc. Japan, 63, (2011), 1027–1037
  GEISSERT, Matthias & HANSEL, Tobias
  
• Asymptotic Behavior of a Leray Solution around a Rotating Obstacle, Progress in Nonlinear Differential Equations and Their Applications, 60, (2011), 251–266
  Galdi, Giovanni P. & Kyed, Mads
  
• Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. Manuscripta Math., 136, (2011), 315–338
  Farwig, Reinhard & Hishida, Toshiaki
  
• Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. Relat. Models, 4, (2010), 569–588
  Suzuki, Masahiro
  
• Asymptotic Structure of a Leray solution to the Navier-Stokes flow around a rotating body, Pacific J. Math., 253, (2011), 367–382
  Farwig, Reinhard; Galdi, Giovanni & Kyed, Mads
  
• Chain homotopy maps for Khovanov homology, J. Knot Theory Ramifications, 20, (2011), 127– 139
  ITO, NOBORU
  
• Finite type invariants of nanowords and nanophrases, Topology Appl., 158, (2011), 1050–1072
  Gibson, Andrew & Ito, Noboru
  
• Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero timedependent boundary values, In: Parabolic Problems: Progr. Nonlineear Differential Equations, 80, (2011), 211–232
  Farwig, R.; Kozono, H. & Sohr, H.
  
• Global weak solutions of the Navier-Stokes system with nonhomogeneous boundary data and divergence, Rend. Semin. Mat. Univ. Padova, 125, (2011), 51–70
  Farwig, Reinhard; Kozono, H. & Sohr, H.
  
• Global well-posedness for Keller-Segel system in Besov type spaces, J. Math. Anal. Appl., 379, (2011), 930–948
  Iwabuchi, Tsukasa
  
• Hierarchy of semiconductor equations: relaxation limits with initial layers for large initial data, MSJ Mem., 26, (2011)
  Nishibata, Shinya & Suzuki, Masahiro
  
• Invariants of Handlebody-Knots via Yokota's Invariants
  A. Mizusawa, J. Murakami
  
• L1-maximal regularity for the Laplacian and applications, Discrete Contin. Dyn. Syst., supplement, 2011, (2011), 495–504
  Y. Giga, J. Saal
  
• Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle, Math. Nachr., 284, (2011), 2065–2077
  Farwig, Reinhard & Hishida, Toshiaki
  
• Leray’s inequality in general multi-connected domains in Rn, Math. Ann., 354, (2012), 137–145
  Farwig, Reinhard; Kozono, Hideo & Yanagisawa, Taku
  
• Non-autonomous Ornstein-Uhlenbeck equations in exterior domains, Adv. Differential Equations, 16, (2011), no. 3-4, 201–220
  T. Hansel, A. Rhandi
  
• On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity, J. Funct. Anal., 260, (2011), no. 7, 2148–2162
  Sawada, Okihiro & Takada, Ryo
  
• On the Navier-Stokes flow with rotating effect and prescribed outflow velocity, J. Math. Fluid Mech., 13, (2011), 405–419
  Hansel, Tobias
  
• On the stationary Navier-Stokes flows around a rotating body, Manuscripta Math., 138, (2012), 315–345
  Heck, Horst; Kim, Hyunseok & Kozono, Hideo
  
• The Influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, Seventh International Symposium on Turbulence and Shear Flows, (2011)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  
• The Influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, Seventh International Symposium on Turbulence and Shear Flows, (2011)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  
• The spin-coating process: analysis of the free boundary value problem, Comm. Partial Differential Equations, 36, (2011), no. 7, 1145–1192
  Denk, Robert; Geissert, Matthias; Hieber, Matthias; Saal, Jürgen & Sawada, Okihiro
  
• The spin-coating process: analysis of the free boundary value problem, Comm. Partial Differential Equations, 36, (2011), no. 7, 1145–1192
  Denk, Robert; Geissert, Matthias; Hieber, Matthias; Saal, Jürgen & Sawada, Okihiro
  
• Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains, J. Evol. Equ., 11, (2011), 485–500
  Farwig, Reinhard & Taniuchi, Yasushi
  
• Weak solutions of the Navier-Stokes system with nonzero boundary values in an exterior domain, In: Math. Analysis of the Navier-Stokes equations and related topics, past and future, Gakuto, Tokyo, 35, (2011), 31–52
  R. Farwig, H. Kozono, F. Riechwald
  
• A description of Bourgain-Pavlovíc’s ill-posedness theorem of the Navier-Stokes equations in the critical Besov space, Harmonic analysis and nonlinear partial differential equations, RIMS Kôkyûroku Bessatsu, B33, Res. Inst. Math. Sci. (RIMS), Kyoto, (2012), 59–85
  O. Sawada
  
• A simple proof of Lq-estimates for the steady–state Oseen and Stokes equations in a rotating frame. Part I: Strong solutions, Proc. Amer. Math. Soc., 141, (2013), 573–583
  Galdi, Giovanni & Kyed, Mads
  
• A simple proof of Lq-estimates for the steady–state Oseen and Stokes equations in a rotating frame. Part II: Weak solutions, Proc. Amer. Math. Soc., 141, (2013), 1313–1322
  Galdi, Giovanni & Kyed, Mads
  
• An approach to rotating boundary layers based on vector radon measures, J. Math. Fluid Mech., (2012), 1–39
  Giga, Yoshikazu & Saal, Jürgen
  
• Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal., 44, (2012), 761–790
  Nishibata, Shinya; Ohnawa, Masashi & Suzuki, Masahiro
  
• Continuous limit of random walks and its application to approximation of nonlinear PDEs, RIMS Kôkyûroku, 1782, (2012), 122–134
  K. Soga
  
• Difference approximation to Aubry-Mather sets of the forced Burgers equation, Nonlinearity, 25, (2012), no. 9, 2401–2422
  Nishida, Takaaki & Soga, Kohei
  
• Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29, (2012), no. 5, 783–812
  Ikoma, Norihisa & Ishii, Hitoshi
  
• Fluid flows around floating bodies, I: The hydrostatic case, J. Math. Fluid Mech., 14, (2012), no. 4, 751–770
  Bemelmans, Josef; Galdi, Giovanni P. & Kyed, Mads
  
• Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, Journal of Difference Equations and Applications, 18, (2012), 1163-1181
  Enatsu, Yoichi; Nakata, Yukihiko; Muroya, Yoshiaki; Izzo, Giuseppe & Vecchio, Antonia
  
• Global existence results for Oldroyd-B fluids in exterior domains, J. Differential Equations, 252, (2012), 2617–2629
  Hieber, Matthias; Naito, Yuka & Shibata, Yoshihiro
  
• Global existence results for Oldroyd-B fluids in exterior domains, J. Differential Equations, 252, (2012), no. 3, 2617–2629
  Hieber, Matthias; Naito, Yuka & Shibata, Yoshihiro
  
• Global stability for a discrete SIS epidemic model with immigration of infectives, Journal of Difference Equations and Applications, 18, (2012), 1913-1924
  Enatsu, Yoichi; Nakata, Yukihiko & Muroya, Yoshiaki
  
• Global well–posedness for the rotating Navier–Stokes–Boussinesq equations with stratification effects, Adv. Math. Sci. Appl., 22, (2012), no. 1, 61–90
  H. Koba, A. Mahalov, T. Yoneda
  
• Growth rate modeling and identification in the crystallization of polymers, Inverse Problems, 28, (2012), 13 pp.
  Liu, Yikan; Xu, Xiang & Yamamoto, Masahiro
  
• Influence of surface tension models on the hydrodynamics of wavy laminar falling films in Volume of Fluid-simulations, Int. J. Multiphase Flow., 43, (2012), 66–71
  Albert, Christoph; Raach, Henning & Bothe, Dieter
  
• Leray’s inequality for fluid flow in symmetric multi-connected two-dimensional domains, Tokyo J. Math., 35, (2012), 63–70
  FARWIG, Reinhard & MORIMOTO, Hiroko
  
• Lp-theory for a generalized nonlinear viscoelastic fluid model of differential type in various domains, Nonlinear Anal., 75, (2012), 5015–5026
  Geissert, Matthias; Götz, Dario & Nesensohn, Manuel
  
• Lp-theory for strong solutions to fluid rigid-body interaction in Newtonian and generalized Newtonian fluids, Trans. Amer. Math. Soc., 365, (2013), 1393–1439
  Geissert, Matthias; Götze, Karoline & Hieber, Matthias
  
• Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model, Nonlinear Analysis: Real World Applications, 13, (2012), 2120-2133
  Enatsu, Yoichi; Nakata, Yukihiko & Muroya, Yoshiaki
  
• Maximal Lp-regularity for a 2D fluid-solid interaction problem, Spectral theory, mathematical system theory, evolution equations, differential and difference equations, Oper. Theory Adv. Appl., Birkhäuser, 221, (2012), 373–384
  Götze, Karoline
  
• Motion of inertial particles in Gaussian fields driven by an infinite-dimensional fractional Brownian motion, Dyn. Syst., 27, (2012), 431–457
  Schöchtel, Georg
  
• On a generalization of the global attractivity for a periodically forced Pielou’s equation, J. of Difference Equations and Applications 18 (2012), 375-396
  Ishihara, Keigo & Nakata, Yukihiko
  
• On nonexistence for stationary solutions to the Navier-Stokes equations with a linear strain, Journal of Mathematical Fluid Mechanics, 15, (2013), 317-333
  Hsu, Pen-Yuan & Maekawa, Yasunori
  
• On radial solutions of inhomogeneous nonlinear scalar field equations, J. of Math. Anal. Appl., 386, (2012), 744–762
  Ikoma, Norihisa
  
• On uniqueness of stationary solutions to the Navier-Stokes equations in exterior domains, Nonlinear Anal., 75, (2012), 3457–3464
  Nakatsuka, Tomoyuki
  
• Propagation of the analyticity for the solution to the Euler equations with nondecaying initial velocity, RIMS Kôkyûroku Bessatsu, B33, (2012), 97–109
  O. Sawada, R. Takada
  
• Qualitative behaviour of solutions for the two–phase Navier–Stokes equations with surface tension, Math. Ann., 356, (2013), no. 2, 737–792
  Köhne, Matthias; Prüss, Jan & Wilke, Mathias
  
• Strong solutions for the interaction of a rigid body and a viscoelastic fluid, J. Math. Fluid Mech., 15, (2013), no. 4, 663–688
  Götze, Karoline
  
• The half-twisted splice operation on reduced knot projections, J. Knot Theory Ramifications, 21, (2012), no. 11, 10 pp.
  ITO, NOBORU & SHIMIZU, AYAKA
  
• The influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, J. Turbulence, 13, (2012)
  Stroh, Alexander; Frohnapfel, Bettina; Hasegawa, Yosuke; Kasagi, Nobuhide & Tropea, Cameron
  
• The influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, J. Turbulence, 13, (2012)
  Stroh, Alexander; Frohnapfel, Bettina; Hasegawa, Yosuke; Kasagi, Nobuhide & Tropea, Cameron
  
• Time periodic solutions to the Navier-Stokes equations in the rotational framework, J. Evol. Equ., 12, (2012), 985–1000
  Iwabuchi, Tsukasa & Takada, Ryo
  
• Weak Neumann implies Stokes, J. Reine Angew. Math., 669, (2012), 75–100
  Geissert, Matthias; Heck, Horst; Hieber, Matthias & Sawada, Okihiro
  
• Weak Neumann implies Stokes, J. Reine Angew. Math., 669, (2012), 75–100
  Geissert, Matthias; Heck, Horst; Hieber, Matthias & Sawada, Okihiro
  
• Analytic rates of solutions to the Euler equations, Discrete Contin. Dyn. Syst. Ser. S, 6, (2013), no. 5, 1409–1415
  Sawada, Okihiro
  
• Analyticity of the Stokes semigroup in spaces of bounded functions, Acta Math., 211, (2013), 1–46
  Abe, Ken & Giga, Yoshikazu
  
• Asymptotic profile of a linearized Navier-Stokes flow past a rotating body, Quart. Appl. Math., 71, (2013), no. 3, 489–500
  Kyed, Mads
  
• Construction of weak solutions of a certain stochastic Navier-Stokes equations, Stochastics, 86, (2014), no. 4, 573–593
  Yokoyama, Satoshi
  
• Dispersive effect of the Coriolis force for the Navier-Stokes equations in the rotational framework, RIMS Kôkyûroku Bessatsu, B42, (2013), 137–152
  T. Iwabuchi, R. Takada
  
• Dynamical braces and dynamical Yang-Baxter map, Journal of Pure and Applied Algebra, 217, (2013), 195-206
  Matsumoto, Diogo Kendy
  
• Existence of minimizers for some coupled nonlinear Schrödinger equations, Geometric properties for parabolic and elliptic PDE’s, Springer INdAM Ser., 2, Springer, Milan, (2013), 143–164
  Ikoma, Norihisa
  
• Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams, Stochastic Process. Appl., 123, (2013), 1229–1275
  Funaki, Tadahisa; Sasada, Makiko; Sauer, Martin & Xie, Bin
  
• Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams, Stochastic Process. Appl., 123, (2013), no. 4, 1229–1275
  Funaki, Tadahisa; Sasada, Makiko; Sauer, Martin & Xie, Bin
  
• Global existence results for Oldroyd-B fluids in exterior domains: the case of non-small coupling parameters, Math. Ann., 357, (2013), 687–709
  Fang, Daoyuang; Hieber, Matthias & Zi, Ruizhao
  
• Global solutions for the Navier-Stokes equations in the rotational framework, Math. Ann., 357, (2013), 727–741
  Iwabuchi, Tsukasa & Takada, Ryo
  
• Hadamard variational formula for the Green function for the velocity and pressure of the Stokes equations, Indiana Univ. Math. J., 62, (2013), 1315–1379
  E. Ushikoshi
  
• Hadamard variational formula for the Green function of the boundary value problem on the Stokes equations, Arch. Ration. Mech. Anal., 208, (2013), no. 3, 1005–1055
  Kozono, Hideo & Ushikoshi, Erika
  
• Invariants of handlebody-knots via Yokota’s invariants, J. Knot Theory Ramifications, 22, (2013), no. 11, 21 pp.
  MIZUSAWA, ATSUHIKO & MURAKAMI, JUN
  
• Linking numbers for handlebody-links, Proc. Japan Acad. Ser. A Math. Sci., 89, (2013), 60–62
  Mizusawa, Atsuhiko
  
• On a class of energy preserving boundary conditions for incompressible Newtonian flows, SIAM J. Math. Anal., 45, (2013), 3768–3822
  Bothe, Dieter; Köhne, Matthias & Prüss, Jan
  
• On a mapping property of the Oseen operator with rotation, Discrete Contin. Dyn. Syst. Ser. S, 6, (2013), no. 5, 1315–1322
  Kyed, Mads
  
• On the multiple hyperbolic systems modeling phase transformation kinetics, Appl. Anal., 93, (2014), 1297–1318
  Liu, Yikan & Yamamoto, Masahiro
  
• On the steady motion of a coupled system solid–liquid, Mem. Amer. Math. Soc., 226, (2013), no. 1060, vi+89 pp.
  Bemelmans, Josef; Galdi, Giovanni P. & Kyed, Mads
  
• Small solutions for nonlinear heat equations, the Navier-Stokes equation, and the Keller-Segel system in Besov and Triebel-Lizorkin spaces, Adv. Differential Equations, 18 (2013), no. 7-8, 687–736
  T. Iwabuchi, M. Nakamura
  
• Survey and remarks on Viro’s definition of Khovanov homology, Geometry of transformation groups and combinatorics, RIMS Kôkyûroku Bessatsu , Res. Inst. Math. Sci. (RIMS), B39, (2013), 9–19
  N. Ito
  
• The L∞-Stokes semigroup in exterior domains, J. Evol. Equ., 14, (2014), 1–28
  Abe, Ken & Giga, Yoshikazu
  
• The Oseen-Navier-Stokes flow in the exterior of a rotating obstacle: The nonautonomous case, J. Reine Angew. Math., 694, (2014), 1–26
  Hansel, Tobias & Rhandi, Abdelaziz
  
• Uniqueness of backward asymptocially almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains, Discrete Contin. Dyn. Syst. Series S, 6, (2013), 1215– 1224
  Farwig, Reinhard & Taniuchi, Yasushi
  
• Uniqueness of steady Navier-Stokes flows in exterior domains, Funkcialaj Ekvacioj, 56, (2013), 323-337
  Nakatsuka, Tomoyuki
  
• A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion, Communications in Partial Differential Equations, 39, (2014), 1906-1935
  Giga, Yoshikazu; Hsu, Pen-Yuan & Maekawa, Yasunori
  
• Concentration-Diffusion phenomena of heat convection in an incompressible fluid, Asymptot. Anal., 88, (2014), 17–41
  Farwig, Reinhard; Schulz, Raphael & Yamazaki, Masao
  
• Concentration-Diffusion phenomena of heat convection in an incompressible fluid, Asymptot. Anal., 88, (2014), 17–41
  Farwig, Reinhard; Schulz, Raphael & Yamazaki, Masao
  
• Decay property for the Timoshenko system with Fourier’s type heat conduction, Hyperbolic Differential Equations, 11, (2014), 135-157
  MORI, NAOFUMI & KAWASHIMA, SHUICHI
  
• Direct numerical simulation of interfacial mass transfer into falling films. Int. J. Heat Mass Tran. 69, (2014), 343-357
  Albert, Christoph; Marschall, Holger & Bothe, Dieter
  
• Dispersive estimates for the Navier-Stokes equations in the rotational framework, Adv. Differential Equations, 19, (2014), 857–878
  Y. Koh, S. Lee , R. Takada
  
• Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force, J. E Equ., 14, (2014), 565–601
  Kozono, Hideo; Mashiko, Yuki & Takada, Ryo
  
• Efficient computation of the flow around single fluid particles using an artificial boundary condition, Internat. J. Numer. Methods Fluids, 75, (2014), 184–204
  Weirich, D.; Köhne, M. & Bothe, D.
  
• Generalized viscoelastic fluids with a free boundary without surface tension, SIAM J. Math. Anal., 46, (2014), no. 1, 428–458
  Nesensohn, Manuel
  
• Global linear stability analysis of falling films with in-and outlet. J. Fluid Mech. 745, (2014), 444-486
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