Weak-Strong Uniqueness for Measure-Valued Solutions

被引：100

作者：

Brenier, Yann ^{[1
]}

De Lellis, Camillo ^{[2
]}

Szekelyhidi, Laszlo, Jr. ^{[3
]}

机构：

[1] Univ Nice, CNRS, FR-2800 Wolfgang Doblin, France

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[3] Univ Bonn, Hausdorff Ctr Math, D-53115 Bonn, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2011年 / 305卷 / 02期

关键词：

VLASOV-POISSON SYSTEM; EULER EQUATIONS; INCOMPRESSIBLE EULER; LIMIT; TIME;

D O I：

10.1007/s00220-011-1267-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：351 / 361

页数：11

共 14 条

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[2]

[Anonymous], 1996, OXFORD LECT SERIES M

[3] On the concept of very weak L2 solutions to Euler'sy equations [J].