Dissipative measure-valued solutions to the Euler-Poisson equation
Analysis of PDEs
2021-09-17 v1
Abstract
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued solutions, i.e., very weak solutions described by a classical Young measure together with appropriate concentration defects. We then investigate the evolution of a relative energy functional to compare a measure-valued solution to a regular solution emanating from the same initial datum. This leads to a (partial) weak-strong uniqueness principle.
Cite
@article{arxiv.2109.07536,
title = {Dissipative measure-valued solutions to the Euler-Poisson equation},
author = {José A. Carrillo and Tomasz Dębiec and Piotr Gwiazda and Agnieszka Świerczewska-Gwiazda},
journal= {arXiv preprint arXiv:2109.07536},
year = {2021}
}