Kinetic and Related Models (KRM)

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

Pages: 75 - 103, Volume 9, Issue 1, March 2016      doi:10.3934/krm.2016.9.75

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Zhenhua Guo - Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an 710069, China (email)
Zilai Li - School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China (email)

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.

Keywords:  Navier-Stokes equations, global existence, free boundary.
Mathematics Subject Classification:  Primary: 35Q35; Secondary: 76N10.

Received: October 2014;      Revised: August 2015;      Available Online: October 2015.