Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary

Mei Wang; Zilai Li; Zhenhua Guo

doi:10.3934/cpaa.2017001

Article Contents

2017, Volume 16, Issue 1: 1-24. Doi: 10.3934/cpaa.2017001

This issue Previous Article Next Article Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations

Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary

1.
School of Sciences, Xi'an University of Technology, Xian 710048, Shaanxi, P. R. China
2.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, Henan Province, P. R. China
3.
Center for Nonlinear Studies and School of Mathematics, Northwest University, Xian 710069, P. R. China

Author Bio: E-mail address: wangmei0439@163.com; E-mail address: zhenhua.guo.math@gmail.com
Zilai Li, E-mail address: lizilai0917@163.com
Zilai Li, E-mail address: lizilai0917@163.com

Received: January 2015

Revised: October 2015

Published: January 2018

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Abstract

In this paper, we obtain the global weak solution to the 3D spherically symmetric compressible isentropic Navier-Stokes equations with arbitrarily large, vacuum data and free boundary when the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda(\rho)=\rho^\beta$ with $\beta>0$. The analysis of the upper and lower bound of the density is based on some well-chosen functionals. In addition, the free boundary can be shown to expand outward at an algebraic rate in time.

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Mathematics Subject Classification: Primary: 35J05, 35J10; Secondary: 35Q30.

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