## Mathematical Physics and Harmonic Analysis Seminar

**Date:** September 14, 2018

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Joonhyun La, Princeton University

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

**Abstract:** In this talk, we prove 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. Main conceptual difficulties include multi-scale nature of the system. We discuss an appropriate notion for the solution for this multi-scale system, and approximation scheme.