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 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 , does not converge in the space of super-critical Sobolev regularity.
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Chenmin Sun 1 ; Nikolay Tzvetkov 1
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@article{CRMATH_2020__358_9-10_989_0,
author = {Chenmin Sun and Nikolay Tzvetkov},
title = {Concerning the pathological set in the context of probabilistic well-posedness},
journal = {Comptes Rendus. Math\'ematique},
pages = {989--999},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {9-10},
year = {2020},
doi = {10.5802/crmath.102},
language = {en},
}
TY - JOUR AU - Chenmin Sun AU - Nikolay Tzvetkov TI - Concerning the pathological set in the context of probabilistic well-posedness JO - Comptes Rendus. Mathématique PY - 2020 SP - 989 EP - 999 VL - 358 IS - 9-10 PB - Académie des sciences, Paris DO - 10.5802/crmath.102 LA - en ID - CRMATH_2020__358_9-10_989_0 ER -
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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