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Communications in Mathematical Physics

, Volume 230, Issue 2, pp 329–363 | Cite as

Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum

  • Tong Yang
  • Changjiang Zhu

Abstract:

 In this paper, we consider the compressible Navier–Stokes equations for isentropic flow of finite total mass when the initial density is either of compact or infinite support. The viscosity coefficient is assumed to be a power function of the density so that the Cauchy problem is well-posed. New global existence results are established when the density function connects to the vacuum states continuously. For this, some new a priori estimates are obtained to take care of the degeneracy of the viscosity coefficient at vacuum. We will also give a non-global existence theorem of regular solutions when the initial data are of compact support in Eulerian coordinates which implies singularity forms at the interface separating the gas and vacuum.

Keywords

Initial Data Cauchy Problem Total Mass Stokes Equation Power Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tong Yang
    • 1
  • Changjiang Zhu
    • 1
  1. 1.Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, P.R. China. E-mail: cjzhu@ccnu.edu.cnCN

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