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

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2010年 / 33卷 / 01期

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

页码：103 / 116

页数：14

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