A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity | Zendy

Dou Changsheng | Zendy; Jiu Quansen | Zendy

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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.

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