Comptes Rendus
no. 3
Partial Differential Equations
Ill-posedness of H1-supercritical waves
[Instabilité des ondes H1-surcritiques]

Présenté par : Gilles Lebeau

Slim Ibrahim1 ; Mohamed Majdoub2 ; Nader Masmoudi3
1 Department of Mathematics & Statistics, Arizona State University, Tempe, AZ 85287-1804, USA
2 Département de mathématiques, faculté des sciences de Tunis, campus universitaire 2092, Tunis, Tunisia
3 The Courant Institute of Mathematical Sciences, NY University, 251 Mercer St., New York, NY 10012, USA
Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 133-138.

Nous étendons les résultats de Lebeau (2005) et Christ et al. (2007) aux cas de nonlinearités surcritiques quelconques. On traite aussi le cas 2D pour des nonlinéarités à croissance exponentielle. La preuve utilise la vitesse finie de propagation et une étude quantitative de l'E.D.O. associée.

We extend the results of Lebeau (2005) and Christ et al. (2007) to more general H1-supercritical nonlinearities. We also extend those results to the 2D case for exponentially growing nonlinearities. The proof uses the finite speed of propagation and a quantitative study of the associated O.D.E. It does not require any scaling invariance of the equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.06.008
Slim Ibrahim 1 ; Mohamed Majdoub 2 ; Nader Masmoudi 3

1 Department of Mathematics & Statistics, Arizona State University, Tempe, AZ 85287-1804, USA
2 Département de mathématiques, faculté des sciences de Tunis, campus universitaire 2092, Tunis, Tunisia
3 The Courant Institute of Mathematical Sciences, NY University, 251 Mercer St., New York, NY 10012, USA 
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Slim Ibrahim; Mohamed Majdoub; Nader Masmoudi. Ill-posedness of $ {H}^{1}$-supercritical waves. Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 133-138. doi : 10.1016/j.crma.2007.06.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.06.008/

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