Large-Time Behavior of the 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum

作     者：Xinyu, Fan Jing, Li Xue, Wang 

作者机构：Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Institute of Applied Mathematics AMSS Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing100190 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Conformal mapping 

摘      要：The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is proportional to a power of the density. Some uniform estimates on the Lp-norm of the density are established, and then deduce that the density converges to its steady state in Lp-spaces, which transforms the large external force into a small one in some sense. Moreover, to deal with the obstacles brought by boundary, the conformal mapping and the pull back Green function are applied to give a point-wise representation of the effective viscous flux, and then make use of slip boundary conditions to cancel out the singularity. Copyright © 2023, The Authors. All rights reserved.