A Geometric approximation to the euler equations: The Vlasov-Monge-Ampere system

被引：18

作者：

Brenier, Y ^{[1
]}

Loeper, G ^{[1
]}

机构：

[1] UMR 6621, F-06108 Nice, France

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2004年 / 14卷 / 06期

关键词：

D O I：

10.1007/s00039-004-0488-1

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

This paper studies the Vlasov - Monge - Ampere system (VMA), a fully non-linear version of the Vlasov - Poisson system (VP) where the ( real) Monge - Ampere equation det partial derivative(2) Psi/partial derivative x(i)partial derivative x(j) = rho substitutes for the usual Poisson equation. This system can be derived as a geometric approximation of the Euler equations of incompressible fluid mechanics in the spirit of Arnold and Ebin. Global existence of weak solutions and local existence of smooth solutions are obtained. Links between the VMA system, the VP system and the Euler equations are established through rigorous asymptotic analysis.

引用

页码：1182 / 1218

页数：37

共 29 条

[1]

Transport equation and Cauchy problem for BV vector fields [J].