论文标题
全球强解决方案和对微麦克罗模型的大量时间行为，可压缩聚合物液位附近的可压缩流体
Global strong solutions and large time behavior to a micro-macro model for compressible polymeric fluids near equilibrium
论文作者
论文摘要
在本文中，我们主要研究全球强溶液的所有阶空间衍生物的长时间衰减速率，用于具有较小初始数据的可压缩聚合物流体的微麦克罗模型。该模型是带有非线性fokker-Planck方程的等粒子可压缩Navier-Stokes方程的耦合。我们首先证明，微麦克罗模型承认了一个独特的全球强解决方案，前提是初始数据接近$ d \ geq2 $的平衡状态。此外，对于$ d \ geq3 $，我们还展示了一个新的关键傅立叶估计，使我们能够为所有订单空间衍生物提供长时间的衰减率。
In this paper, we mainly study the global strong solutions and its long time decay rates of all order spatial derivatives to 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 $d\geq2$. Moreover, for $d\geq3$, we also show a new critical Fourier estimation that allow us to give the long time decay rates of $L^2$ norm for all order spatial derivatives.
