|Title||Weak-strong uniqueness for measure-valued Solutions|
|Publication Type||Journal Article|
|Year of Publication||2011|
|Authors||Brenier Y., De Lellis C., L. Székelyhidi Jr.|
|Journal||Communications in Mathematical Physics|
|Type of Article||euler and navier-stokes equations|
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 , 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 con- servation laws have the weak-strong uniqueness property.
Comm. Math. Phys. 305 (2011), 351-361