Calculus of Variations and Geometric Measure Theory

Y. Brenier - C. De Lellis - L. J. Székelyhidi

Weak-strong uniqueness for measure-valued Solutions

created by delellis on 06 May 2011
modified on 02 Jul 2013


Published Paper

Inserted: 6 may 2011
Last Updated: 2 jul 2013

Journal: Comm. Math. Phys.
Volume: 305
Number: 2
Pages: 351-361
Year: 2011

For the update version and eventual errata see the webpage http:/www.math.uzh.chdelellis


We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda in their landmark paper \cite{DiPernaMajda}, where in particular global existence to any $L^2$ 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.