On the dynamics of Navier-Stokes equations for a shallow water model

被引:20
|
作者
Duan, Qin [1 ]
机构
[1] Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China
关键词
Compressible Navier-Stokes equations; Density-dependent viscosity; Shallow water model; Free boundary; Vacuum; DENSITY-DEPENDENT VISCOSITY; ONE-DIMENSIONAL MOTION; HEAT-CONDUCTING GAS; DEGENERATE VISCOSITY; COMPRESSIBLE FLOWS; INITIAL DATA; VACUUM; COEFFICIENT; EXISTENCE; BEHAVIOR;
D O I
10.1016/j.jde.2011.01.010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study a free boundary problem of one-dimensional compressible Navier-Stokes equations with a density-dependent viscosity, which include, in particular, a shallow water model. Under some suitable assumptions on the initial data, we obtain the global existence, uniqueness and the large time behavior of weak solutions. In particular, it is shown that a stationary wave pattern connecting a gas to the vacuum continuously is asymptotically stable for small initial general perturbations. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:2687 / 2714
页数:28
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