Student Probability/PDE Seminar: Some Non-Uniqueness Results for PDEs from Hamiltonian Systems

Seminar | October 12 | 2:10-3:30 p.m. | 891 Evans Hall

 Stamatis Dostoglou, University of Missouri

 Department of Mathematics

We shall first recall how to obtain macroscopic PDEs by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. We shall then construct along these lines explicit examples of spontaneous energy generation (and therefore establish non-uniqueness) for the compressible Euler system, with and without pressure. The examples come from rescalings of well-posed deterministic systems of molecules that either collide elastically or interact via singular pair potentials. They live in space dimension 1 for the Euler with pressure and in higher dimensions, but have singular support, for the pressureless Euler. (Work with Jianfei Xue.)