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 (CommunMath Phys 108(4): 667-689, 1987), 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.
Weak-Strong Uniqueness for Measure-Valued Solutions
de Lellis, C.;
2011-01-01
Abstract
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 (CommunMath Phys 108(4): 667-689, 1987), 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.File in questo prodotto:
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