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Compressible Navier–Stokes equations with vacuum state in the case of general pressure law

✍ Scribed by Daoyuan Fang; Ting Zhang

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 190 KB
Volume: 29
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.708

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✦ Synopsis

Abstract

In this paper, we consider the one‐dimensional compressible isentropic Navier–Stokes equations with a general ‘pressure law’ and the density‐dependent viscosity coefficient when the density connects to vacuum continuously. Precisely, the viscosity coefficient µ is proportional to ρ^θ^ and 0<θ<1, where ρ is the density. And the pressure P = P(ρ) is a general ‘pressure law’. The global existence and the uniqueness of weak solutions is proved, and a decay result for the pressure as t→ + ∞ is given. It is also proved that no vacuum states and no concentration states develop, and the free boundary do not expand to infinite. Copyright © 2006 John Wiley & Sons, Ltd.

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