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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.