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Weak-strong uniqueness for measure-valued solutions


Brenier, Yann; De Lellis, Camillo; Székelyhidi Jr., László (2011). Weak-strong uniqueness for measure-valued solutions. Communications in Mathematical Physics, 305(2):351-361.

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 in their landmark paper [10], 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.

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 in their landmark paper [10], 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics
Language:English
Date:2011
Deposited On:11 Aug 2011 14:50
Last Modified:23 Aug 2021 16:32
Publisher:Springer
ISSN:0010-3616
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00220-011-1267-0
Related URLs:http://arxiv.org/abs/0912.1028v1

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