Global existence of weak solution to the free boundary problem for compressible  Navier-Stokes

Zhenhua  Guo; Zilai  Li

doi:10.3934/krm.2016.9.75

Article Contents

2016, Volume 9, Issue 1: 75-103. Doi: 10.3934/krm.2016.9.75

This issue Previous Article Asymptotic preserving scheme for a kinetic model describing incompressible fluids Next Article Kinetic derivation of fractional Stokes and Stokes-Fourier systems

Global existence of weak solution to the free boundary problem for compressible Navier-Stokes

Zhenhua Guo^1, and
Zilai Li^2,

1.
Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an 710069
2.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000

Received: October 2014

Revised: August 2015

Published: March 2016

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Abstract

In this paper, the compressible Navier-Stokes system (CNS) with constant viscosity coefficients is considered in three space dimensions. we prove the global existence of spherically symmetric weak solutions to the free boundary problem for the CNS with vacuum and free boundary separating fluids and vacuum. In addition, the free boundary is shown to expand outward at an algebraic rate in time.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76N10.

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