Global Behavior of Compressible Navier-Stokes Equations with a Degenerate Viscosity Coefficient

Article

DOI: 10.1007/s00205-006-0425-6

Cite this article as:
Zhang, T. & Fang, D. Arch Rational Mech Anal (2006) 182: 223. doi:10.1007/s00205-006-0425-6

Abstract

In this paper, we study a free boundary problem for compressible Navier-Stokes equations with density-dependent viscosity. Precisely, the viscosity coefficient μ is proportional to ρθ with https://static-content.springer.com/image/art%3A10.1007%2Fs00205-006-0425-6/MediaObjects/s00205-006-0425-6flb1.gif, where ρ is the density, and γ > 1 is the physical constant of polytropic gas. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the weak solution, give the uniform bounds (with respect to time) of the solution and show that it converges to a stationary one as time tends to infinity. Moreover, we estimate the stabilization rate in L norm, (weighted) L2 norm and weighted H1 norm of the solution as time tends to infinity.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouPR China