Calculus of Variations and Geometric Measure Theory

F. Cavalletti - M. Sedjro - M. Westdickenberg

A Variational Time Discretization for Compressible Euler Equations

created by cavallett on 22 Oct 2014
modified on 07 Nov 2018


Accepted Paper

Inserted: 22 oct 2014
Last Updated: 7 nov 2018

Journal: Trans. AMS
Year: 2014


We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep 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.