A geometric approximation to the Euler equations: the Vlasov-Monge-Ampere system
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
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 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.
Keywords
Cite
@article{arxiv.math/0504135,
title = {A geometric approximation to the Euler equations: the Vlasov-Monge-Ampere system},
author = {Yann Brenier and Gregoire Loeper},
journal= {arXiv preprint arXiv:math/0504135},
year = {2007}
}