English

Weak-strong uniqueness for measure-valued solutions

Analysis of PDEs 2009-12-08 v1

Abstract

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda, and in particular global existence to any L2 initial data was proven. Whether measure-valued solutions agree with classical solutions if the latter exist has apparently remained open. We also show that DiPerna's measure-valued solutions to systems of conservation laws have the weak-strong uniqueness property.

Keywords

Cite

@article{arxiv.0912.1028,
  title  = {Weak-strong uniqueness for measure-valued solutions},
  author = {Yann Brenier and Camillo De Lellis and László Székelyhidi},
  journal= {arXiv preprint arXiv:0912.1028},
  year   = {2009}
}
R2 v1 2026-06-21T14:20:01.471Z