A remark on free boundary problem of 1-D compressible Navier-Stokes equations with density-dependent viscosity

被引:10
|
作者
Dou, Changsheng [1 ]
Jiu, Quansen [1 ]
机构
[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
关键词
compressible Navier-Stokes equations; free boundary problem; weak solutions; existence and uniqueness; HEAT-CONDUCTIVE FLUIDS; SYMMETRIC-SOLUTIONS; ISENTROPIC FLUIDS; SMOOTH SOLUTIONS; VACUUM; COEFFICIENT; EXISTENCE; MOTION; GAS;
D O I
10.1002/mma.1154
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 pi(rho) = rho(theta) with 0 is an element of (0, gamma/2], gamma > 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 (C) 2009 John Wiley & Sons, Ltd.
引用
收藏
页码:103 / 116
页数:14
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