Weak-Strong Uniqueness for Measure-Valued Solutions

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by DiPerna and Majda in their landmark paper (Commun Math Phys 108(4):667–689, 1987), where 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.

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