Analysis of complex and non-smooth flows
Final Report Abstract
The project comprises four subprojects adressing some fundamental problems in mathematical fluid dynamics as well as the development of functional analytic methods and tools for their treatment. The four projects are: (1) Multiplication and Nemytskij operators in anisotropic function spaces; (2) Heterogeneous catalysis; (3) Stokes equations on domains with edges and vertices; (4) Dynamic contact lines. Subproject (1) yields an important tool for the treatment of nonlinear, i.p. quasilinear, problems such as considered in subprojects (2) and (4). In fact, by the lack of smoothness and integrability for the treatment of the contact line model in (4) in the Lp -setting, it is crucial to get the optimal value for p which can only be provided by the detailed analysis on multiplication of anisotropic function spaces given in (1). Even though theory on domains with edges and vertices for classical elliptic and parabolic PDE is well-developed, corresponding results for the Stokes equations are still very rare. Particularly, for the instationary Stokes system only very few results exist. Subproject (3) provides results in this direction for a large class of boundary conditions on wedge type domains. Results of this type represent also the key ingredient for an analytical approach to models describing contact line movement as considered in (4). In connection with other recent developments on the topic, fundamental progress in these directions has been obtained. Subprojects (1) and (3) also include basic tools for an approach to further complex flows. In the context of subproject (2) stability of a model describing heterogeneous catalysis was proved. Summarizing, substantial progress in the analysis of non-smooth flows, i.p. of dynamic contact lines, and of complex flows such as models describing heterogeneous catalysis has been achieved.
Publications
-
Optimal Regularity for the Stokes Equations on a 2D Wedge Domain Subject to Perfect Slip, Dirichlet and Navier Boundary Conditions. PhD Thesis, HHU, u Shaker Verlag, 2021.
L. Westermann
-
Multiplication in vector‐valued anisotropic function spaces and applications to non‐linear partial differential equations. Mathematische Nachrichten, 295(9), 1709-1754.
Köhne, Matthias & Saal, Jürgen
-
Stable and unstable flow regimes for active fluids in the periodic setting. Nonlinear Analysis: Real World Applications, 69, 103707.
Bui, Christiane; Gesse, Christian & Saal, Jürgen
-
Stability Analysis for a Class of Heterogeneous Catalysis Models. Dynamics of Partial Differential Equations, 21(4), 351-365.
Gesse, Christian; Köhne, Matthias & Saal, Jürgen
