Incompressible Euler limits from a nonlinear Vlasov–Fokker–Planck equation with constant temperature

Abstract

We consider the incompressible Euler limit of a nonlinear Vlasov–Fokker–Planck equation with constant temperature, under a regime where the Strouhal and Knudsen numbers scale as St=ɛ and Kn=ɛq for q>1. Using relative entropy methods and uniform moment bounds, we show that weak solutions converge to dissipative solutions of the incompressible Euler equations on the torus.