A VARIATIONAL TIME DISCRETIZATION FOR COMPRESSIBLE EULER EQUATIONS

被引：10

作者：

Cavalletti, Fabio ^{[1
]}

Sedjro, Marc ^{[2
]}

Westdickenberg, Michael ^{[3
]}

机构：

[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy

[2] AIMS Tanzania, Plot 288,Makwahiya St,Regent Estate, Dar Es Salaam, Tanzania

[3] Rhein Westfal TH Aachen, Lehrstuhl Math Anal, Templergraben 55, D-52062 Aachen, Germany

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 371卷 / 07期

关键词：

Compressible gas dynamics; optimal transport; ISENTROPIC GAS-DYNAMICS; WELL-POSEDNESS; CONSERVATION-LAWS; OPTIMAL TRANSPORT; ENTROPY SOLUTIONS; POISSON SYSTEMS; WEAK SOLUTIONS; CONVERGENCE; DISSIPATION; FORMULATION;

D O I：

10.1090/tran/7747

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a variational time discretization for the multidimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each time step requires the minimization of a functional measuring the acceleration of fluid elements, over the cone of monotone transport maps. We prove convergence to measure-valued solutions for the pressureless gas dynamics and the compressible Euler equations. For one space dimension, we obtain sticky particle solutions for the pressureless case.

引用

页码：5083 / 5155

页数：73

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