A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity |
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Authors: | Changsheng Dou Quansen Jiu |
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Affiliation: | School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China |
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Abstract: | In this paper, we prove the existence and uniqueness of the weak solution of the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity µ(ρ)=ρθ with θ∈(0, γ?2], γ>1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one‐dimensional Siant–Venant model of shallow water and generalize ones in (Arch. Rational Mech. Anal. 2006; 182: 223–253). Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | compressible Navier– Stokes equations free boundary problem weak solutions existence and uniqueness |
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