Weak-Strong Uniqueness for Measure-Valued Solutions

Communications in Mathematical Physics

Volumn 305, Issue 2, 2011, Pages 351-361

  Brenier, Yann ^a   de Lellis, Camillo ^b   Székelyhidi Jr , László ^c  

^a CNRS   (France)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79957970115     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-011-1267-0     Document Type: Article

References (14)

1. Alibert J. J., Bouchitte G.: Non-uniform integrability and generalized young measure. J. Convex Anal. 4(1), 129-147 (1997).
2. 2 solutions to Euler's equations. SIAM J. Math. Anal. 33(5), 995-1006 (2002) (electronic).
3. Brenier Y.: Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Part. Diff. Eqs. 25(3-4), 737-754 (2000).
4. Brenier Y., Grenier E.: Limite singulière du système de Vlasov-Poisson dans le régime de quasi neutralité: le cas ind'ependant du temps. C. R. Acad. Sci. Paris Sér. I Math. 318(2), 121-124 (1994).
5. Constantin P.: Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations. Commun. Math. Phys. 104(2), 311-326 (1986).
6. Dafermos, C. M.: Hyperbolic conservation laws in continuum physics, Second ed., Vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 2005.
7. De Lellis C., Székelyhidi L. Jr.: The Euler equations as a differential inclusion. Ann. Math. (2) 170(3), 1417-1436 (2009).
8. De Lellis C., Székelyhidi L. Jr.: On admissibility criteria for weak solutions of the Euler equations. Arch. Rat. Mech. Anal. 195(1), 225-260 (2010).
9. Di Perna R. J.: Measure-valued solutions to conservation laws. Arch. Rat. Mech. Anal. 88(3), 223-270 (1985).
10. DiPerna R. J., Majda A. J.: Oscillations and concentrations in weak solutions of the incompressible fluid equations. Commun. Math. Phys. 108(4), 667-689 (1987).
11. Lions, P.-L.: Mathematical topics in fluid mechanics. Vol. 1, Vol. 3 of Oxford Lecture Series in Mathematics and its Applications. New York: The Clarendon Press, Oxford University Press, 1996.
12. Masmoudi N.: Remarks about the inviscid limit of the Navier-Stokes system. Commun. Math. Phys. 270(3), 777-788 (2007).
13. Scheffer V.: An inviscid flow with compact support in space-time. J. Geom. Anal. 3(4), 343-401 (1993).
14. Shnirelman A.: On the nonuniqueness of weak solution of the Euler equation. Comm. Pure Appl. Math. 50(12), 1261-1286 (1997).