Comptes Rendus
no. 9-10
Équations aux dérivées partielles
Concerning the pathological set in the context of probabilistic well-posedness
Chenmin Sun1 ; Nikolay Tzvetkov1 
1 Université de Cergy-Pontoise, Laboratoire de Mathématiques AGM, UMR 8088 du CNRS, 2 av. Adolphe Chauvin 95302 Cergy-Pontoise Cedex, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 989-999.

On démontre un résultat complémentaire à ceux manifestant le caractère bien posé probabiliste de l’équation des ondes avec des données initiales de régularité de Sobolev super critique par rapport au changement d’échelle laissant invariant l’équation.

We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set S of the Sobolev space of super-critical regularity such that (in sharp contrast with the probabilistic well-posedness results) the family of global smooth solutions, generated by the convolution with some approximate identity of the elements of S, does not converge in the space of super-critical Sobolev regularity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.102
Chenmin Sun 1 ; Nikolay Tzvetkov 1

1 Université de Cergy-Pontoise, Laboratoire de Mathématiques AGM, UMR 8088 du CNRS, 2 av. Adolphe Chauvin 95302 Cergy-Pontoise Cedex, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Chenmin Sun; Nikolay Tzvetkov. Concerning the pathological set in the context of probabilistic well-posedness. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 989-999. doi : 10.5802/crmath.102. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.102/

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