STEADY SOLUTIONS TO VISCOUS SHALLOW WATER EQUATIONS. THE CASE OF HEAVY WATER

被引：2

作者：

Axmann, Simon ^{[1
]}

Mucha, Piotr Boguslaw ^{[2
]}

Pokorny, Milan ^{[1
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Sokolovska 83, Prague 18675 8, Czech Republic

[2] Univ Warsaw, Inst Appl Math & Mech, Ul Banacha 2, PL-02097 Warsaw, Poland

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2017年 / 15卷 / 05期

关键词：

steady compressible Navier-Stokes system; shallow water equation; low Mach number limit; density dependent viscosities; large data; existence via Schauder type fixed point theorem; NAVIER-STOKES EQUATIONS; MACH NUMBER LIMIT; DOMAINS; FLOWS; EXISTENCE; PIPE;

D O I：

10.4310/CMS.2017.v15.n5.a8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we are able to construct a solution, provided the total mass is sufficiently large. The main mathematical part is located in the construction of solutions. Uniqueness is impossible to obtain, since the gradient of the velocity is of magnitude of the force. The investigation is connected to the corresponding singular limit as Mach number goes to zero and methods for weak solutions to the compressible Navier-Stokes system.

引用

页码：1385 / 1402

页数：18

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