No. 2019.01
A variational time discretization for compressible Euler equations
F. Cavalletti, M. Sedjro, and M. Westdickenberg
Subject: Compressible gas dynamics, optimal transport


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.


Trans. Amer. Math. Soc. 371 (2019), 5083-5155