Phragmen-Lindelof alternative results for the shallow water equations for transient compressible viscous flow

被引：2

作者：

Liu, Yan ^{[1
]}

Chen, Yuanlong ^{[1
]}

Luo, Changri ^{[2
]}

Lin, Changhao ^{[3
]}

机构：

[1] Guangdong Univ Finance, Dept Appl Math, Guangzhou 510521, Guangdong, Peoples R China

[2] Cent China Normal Univ, Dept Comp Sci, Wuhan 430079, Hubei, Peoples R China

[3] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 398卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Shallow water equations; Transient compressible viscous flow; Phragmen-Lindelof alternative; Saint-Venant's Principle; SPATIAL DECAY BOUNDS; NAVIER-STOKES EQUATIONS; GLOBAL EXISTENCE; CAUCHY-PROBLEM;

D O I：

10.1016/j.jmaa.2012.08.054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the spatial behavior of the viscous shallow water equations in a two-dimensional channel domain is studied. A differential inequality for suitable energy associated with the solutions of the viscous shallow water equations in a semi-infinite channel is derived, from which we show the Phragmen-Lindelof alternative results. The main tool used is the energy method. Our results can be viewed as a version of Saint-Venant's principle to the transient compressible viscous flow. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：409 / 420

页数：12

共 31 条

[1] DECAY-ESTIMATES IN STEADY PIPE-FLOW
AMES, KA
PAYNE, LE
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (04) : 789 - 815
[2] SPATIAL DECAY-ESTIMATES IN TIME-DEPENDENT STOKES-FLOW
AMES, KA
PAYNE, LE
SCHAEFER, PW
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (06) : 1395 - 1413
[3] Amick CJ., 1977, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, V4, P473
[4] [Anonymous], S INT APPL AN FIZ MA
[5] Boley B.A., 1958, P 3 US NAT C APPL ME, P259
[6] Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
Bresch, D
Desjardins, B
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 238 (1-2) : 211 - 223
[7] Hardy C.H., 1953, INEQUALITIES
[8] Horgan C.O., 1989, APPL MECH REV, V42, P295, DOI DOI 10.1115/1.3152414
[9] SPATIAL DECAY-ESTIMATES IN TRANSIENT HEAT-CONDUCTION
HORGAN, CO
PAYNE, LE
WHEELER, LT
[J]. QUARTERLY OF APPLIED MATHEMATICS, 1984, 42 (01) : 119 - 127
[10] RECENT DEVELOPMENTS CONCERNING SAINT-VENANT PRINCIPLE
HORGAN, CO
KNOWLES, JK
[J]. ADVANCES IN APPLIED MECHANICS, 1983, 23 : 179 - 269

← 1 2 3 4 →