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A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity
Author(s) -
Dou Changsheng,
Jiu Quansen
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1154
Subject(s) - uniqueness , mathematics , compressibility , viscosity , mathematical analysis , boundary value problem , perturbation (astronomy) , navier–stokes equations , boundary (topology) , mechanics , thermodynamics , physics , quantum mechanics
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)=ρ θ 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.