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arXiv · 2409.00386

Free boundary value problem for the radial symmetric compressible isentropic Navier-Stokes equations with density-dependent viscosity

Xiangdi Huang·Weili Meng·Anchun Ni
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Abstract

This paper is devoted to the study of free-boundary-value problem of the compressible Naiver-Stokes system with density-dependent viscosities $μ=const>0,λ=ρ^β$ which was first introduced by Vaigant-Kazhikhov \cite{1995 Vaigant-Kazhikhov-SMJ} in 1995. By assuming the endpoint case $β=1$ in the radially spherical symmetric setting, we prove the (a priori) expanding rate of the free boundary is algebraic for multi-dimensional flow, and particularly establish the global existence of strong solution of the two-dimensional system for any large initial data. This also improves the previous work of Li-Zhang \cite{2016 Li-Zhang-JDE} where they proved the similar result for $β>1$. The main ingredients of this article is making full use of the geometric advantange of domain as well as the critical space dimension two.

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Xiangdi Huang, Weili Meng, Anchun Ni. 2024-08-31. Free boundary value problem for the radial symmetric compressible isentropic Navier-Stokes equations with density-dependent viscosity. https://arxiv.org/abs/2409.00386

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