Global well posedness of 2D diffusive Fokker-Planck-Navier-Stokes systems

Global well posedness of 2D diffusive Fokker-Planck-Navier-Stokes systems

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Joonhyun La, Princeton University
Fine Hall 322

In this talk, we will see that there is a unique global strong solution to the 2D Navier-Stokes system coupled with diffusive Fokker-Planck equation of a Hookean type potential. This system regards a polymeric fluid as a dilute suspension of polymers in an incompressible solvent, which is governed by the Navier-Stokes equation, and distribution of polymer configuration is governed by the Fokker-Planck equation, where spatial diffusion effects of polymers are also considered. Well-known Oldroyd-B models can be rewritten in the form of this system. We will discuss an appropriate notion for the solution for this multiscale system, and we will discuss how to find such solution.