Global Classical Solutions to a Compressible Model for Micro-Macro Polymeric Fluids Near Equilibrium

Abstract

In this paper we first employ the energetic variational method to derive a micromacro model for compressible polymeric fluids. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We then prove the global in time existence of the smooth solution near the global equilibrium.

Global strong solutions and optimal $L^2$ decay to the compressible FENE dumbbell model

“…Ning, Y. Liu and T. Zhang [18] proved the first global well-posedness for (1.1) if the initial data is close to the equilibrium. In [18], the authors assume that R ∈ R 3 which means that polymer elongation can be infinite. Actually, the polymer elongation R is usually bounded.…”

Global solutions and large time behavior for some Oldroyd-B type models in $R^2$

“…The appearance of the term q ∇ q g 2 H s−1 (L 2 ) forces us to consider mixed derivative estimates just as what have been shown in [25] and [14]. Applying Λ m to (3.36) and taking L 2 (L 2 ) inner product with q 2 Λ m g, m = 0, s, we deduce that…”

Global strong solutions and large time behavior to the compressible co-rotation FENE dumbbell model of polymeric flows near equilibrium

“…The well-posedness for the system (1.1) was established by J. Ning, Y. Liu and T. Zhang [16]. They proved the global well-posedness for (1.1) if the initial data is close to the equilibrium.…”

“…They proved the global well-posedness for (1.1) if the initial data is close to the equilibrium. In [16], the authors assume that R ∈ R 3 which means that polymer elongation may be infinite.…”

“…In this paper we consider the compressible co-rotation finite extensible nonlinear elastic (FENE) dumbbell model [1,12,16]:…”