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arXiv · 2201.08655

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

Wenjie Deng·Wei Luo·Zhaoyang Yin
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Abstract

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.

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Wenjie Deng, Wei Luo, Zhaoyang Yin. 2022-01-21. Global strong solutions and large time behavior to a micro-macro model for compressible polymeric fluids near equilibrium. https://arxiv.org/abs/2201.08655

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