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

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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 ρ θ with , 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) L 2 norm and weighted H 1 norm of the solution as time tends to infinity.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, PR China

    Ting Zhang & Daoyuan Fang

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  1. Ting Zhang
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  2. Daoyuan Fang
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Correspondence to Ting Zhang.

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Communicated by T-P Liu

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Zhang, T., Fang, D. Global Behavior of Compressible Navier-Stokes Equations with a Degenerate Viscosity Coefficient. Arch Rational Mech Anal 182, 223–253 (2006). https://doi.org/10.1007/s00205-006-0425-6

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  • DOI: https://doi.org/10.1007/s00205-006-0425-6

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