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 well-posedness and the L 2 decay rate for the strong solutions of a micro-macro model for compressible polymeric fluids with small initial data. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We first prove that the micro-macro model admits a unique global strong solution provided the initial data are close to equilibrium state for d ≥ 2. Moreover, we obtain the L 2 decay rate of global strong solutions for d ≥ 3 with Hookean spring by using Fourier splitting method. Finally, we obtain the Ḣs decay rate by establishing a new fourier splitting estimate.