AN INTERFACE PROBLEM: THE TWO-LAYER SHALLOW WATER EQUATIONS

被引：3

作者：

Petcu, Madalina ^{[1
,2
]}

Temam, Roger ^{[3
]}

机构：

[1] Univ Poitiers, Lab Math & Applicat, F-86962 Futuroscope, France

[2] Romanian Acad, Inst Math, Bucharest, Romania

[3] Indiana Univ, Inst Sci Comp & Appl Math, Bloomington, IN 47405 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 11-12期

基金：

美国国家科学基金会;

关键词：

Shallow water equations; two layers fluid; transparent boundary conditions; strictly dissipative boundary conditions; ABSORBING BOUNDARY-CONDITIONS; ISENTROPIC GAS-DYNAMICS; 3D PRIMITIVE EQUATIONS; EXISTENCE; CONVERGENCE; VISCOSITY; SYSTEMS;

D O I：

10.3934/dcds.2013.33.5327

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this article is to study a model of two superposed layers of fluid governed by the shallow water equations in space dimension one. Under some suitable hypotheses the governing equations are hyperbolic. We introduce suitable boundary conditions and establish a result of existence and uniqueness of smooth solutions for a limited time for this model.

引用

页码：5327 / 5345

页数：19

共 47 条

[1]

[Anonymous], 1985, DUKE U MATH SERIES

[2] A multilayer Saint-Venant model: Derivation and numerical validation [J].

Audusse, E .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2005, 5 (02) :189-214

[3]

Benzoni-Gavage S., 2007, Multidimensional Hyperbolic Partial Differential Equations. First-Order Systems and Applications Oxford Mathematical Monographs

[4] A ROBUST WELL-BALANCED SCHEME FOR MULTI-LAYER SHALLOW WATER EQUATIONS [J].

Bouchut, Francois ;

Zeitlin, Vladimir .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2010, 13 (04) :739-758

[5] Boundary Conditions for Limited Area Models Based on the Shallow Water Equations [J].

Bousquet, Arthur ;

Petcu, Madalina ;

Shiue, Ming-Cheng ;

Temam, Roger ;

Tribbia, Joseph .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (03) :664-702

[6] Existence theory for the isentropic Euler equations [J].

Chen, GQ ;

LeFloch, PG .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2003, 166 (01) :81-98

[7]

Chen Q., 2009, J SCI COMPUTING

[8] NUMERICAL APPROXIMATION OF THE INVISCID 3D PRIMITIVE EQUATIONS IN A LIMITED DOMAIN [J].

Chen, Qingshan ;

Shiue, Ming-Cheng ;

Temam, Roger ;

Tribbia, Joseph .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (03) :619-646

[9] Analysis of the semi-geostrophic shallow water equations [J].

Cullen, M. J. P. .

PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (10-12) :1461-1465

[10] CONVERGENCE OF THE VISCOSITY METHOD FOR ISENTROPIC GASDYNAMICS [J].

DIPERNA, RJ .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 91 (01) :1-30

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