Global strong solutions and large time behavior to a micro-macro model for compressible polymeric fluids near equilibrium

Abstract

In this paper, we mainly study the global strong solutions to a micro-macro model for compressible polymeric fluids with small initial data and their long-time decay rates of all order spatial derivatives. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We first present that the micro-macro model admits a unique global strong solution provided the initial data are close to equilibrium state for d≥2. Moreover, for d≥3, we show a new critical Fourier estimation that allows us to derive the long-time decay rates of the L2 norm for all order spatial derivatives.