Calculus of Variations and Geometric Measure Theory

F. Cavalletti - M. Sedjro - M. Westdickenberg

A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations

created by cavallett on 13 Nov 2013
modified on 08 Sep 2014


Accepted Paper

Inserted: 13 nov 2013
Last Updated: 8 sep 2014

Journal: SIAM J. Math. Anal.
Year: 2013


Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savar\'{e}. Their proof uses a discrete particle approximation and stability properties for first order differential inclusions. Here we give a more direct proof that relies on a result by Haraux on the differentiability of metric projections. We apply the same method also to the one-dimensional Euler-Poisson system, obtaining a new proof for the global existence of weak solutions.

Keywords: Optimal transport, Pressureless Gas Dynamics