Project Details
Projekt
Rough and nonlinear transport in stochastic fluid dynamics
Applicants
Professor Dr. Benjamin Gess; Rishabh Gvalani, Ph.D.
Subject Area
Mathematics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 526086093
The two guiding landmarks of this proposal are as follows: (1) Rough stochastic transport: We propose to study the long-time behavior and mixing properties of passive scalars driven by rough random velocity fields, in particular by the velocity fields of the Kraichnan model. This will entail the development of a random dynamical systems (RDS) approach to stochastic differential equations (SDEs) with irregular coefficients. (2) Nonlinear stochastic transport: Secondly, we aim to study nonlinear transport equations driven by random velocity fields including their rigorous derivation from microscopic descriptions and their long-time behavior and mixing properties. This includes the development of an RDS approach to McKean-Vlasov SDEs.
DFG Programme
Priority Programmes
Subproject of
SPP 2410:
Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa)
International Connection
Switzerland
