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Compressible Navier–Stokes equations with vacuum state in the case of general pressure law
Author(s) -
Fang Daoyuan,
Zhang Ting
Publication year - 2005
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.708
Subject(s) - uniqueness , compressibility , mathematics , isentropic process , viscosity , boundary (topology) , law , mathematical analysis , state (computer science) , pressure coefficient , navier–stokes equations , thermodynamics , physics , algorithm , political science
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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