Almost everywhere well-posedness of continuity equations with measure initial data

Luigi Ambrosio; Alessio Figalli

doi:10.1016/j.crma.2010.01.018

Mathematical Analysis/Probability Theory

Almost everywhere well-posedness of continuity equations with measure initial data
[Existence « presque partout » des équations de continuité avec données initiales mesures]

Présenté par : Pierre-Louis Lions

Luigi Ambrosio ¹ ; Alessio Figalli ²

¹ Scuoli Normale Superiore, piazza Cavalieri 7, 56126 Pisa, Italy
² Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, USA

Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 249-252.

Résumé
Abstract

Dans cette Note, nous présentons des nouveaux résultats concernant l'existence, l'unicité (au sens « presque partout ») et la stabilité pour des équations de continuité avec données initiales mesures. Les preuves de tous ces résultats sont données dans Ambrosio et al. [4], avec aussi des applications à la limite semiclassique pour l'équation de Schrödinger.

The aim of this Note is to present some new results concerning “almost everywhere” well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in Ambrosio et al. [4], together with some application to the semiclassical limit of the Schrödinger equation.

Reçu le : 2009-10-14
Accepté le : 2010-01-13
Publié le : 2010-02-21

DOI : 10.1016/j.crma.2010.01.018

Affiliations des auteurs :

Luigi Ambrosio ¹ ; Alessio Figalli ²

¹ Scuoli Normale Superiore, piazza Cavalieri 7, 56126 Pisa, Italy
² Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, USA

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     pages = {249--252},
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Luigi Ambrosio; Alessio Figalli. Almost everywhere well-posedness of continuity equations with measure initial data. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 249-252. doi : 10.1016/j.crma.2010.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.018/

Bibliographie
Cité par

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[9] A. Figalli, T. Paul, work in preparation

[10] P. Gérard, Mesures semi-classiques et ondes de Bloch, in: Seminaire sur les Équations aux Dérivées Partielles, 1990–1991. Exp. No. XVI, 19 pp., École Polytechnique, Palaiseau, 1991

[11] P.L. Lions; T. Paul Sur les mesures de Wigner, Rev. Mat. Iberoamericana, Volume 9 (1993), pp. 553-618

[12] P.L. Lions Mathematical Topics in Fluid Mechanics, vol. I: Incompressible Models, Oxford Lecture Series in Mathematics and Its Applications, vol. 3, Oxford University Press, 1996

[13] P.L. Lions Mathematical Topics in Fluid Mechanics, vol. II: Compressible Models, Oxford Lecture Series in Mathematics and Its Applications, vol. 10, Oxford University Press, 1998

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