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arXiv · 2310.15520

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

Xinyu Fan·Jing Li·Xue Wang
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Abstract

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.

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Xinyu Fan, Jing Li, Xue Wang. 2023-10-24. Large-Time Behavior of the 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum. https://arxiv.org/abs/2310.15520

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