Construction of blow-up solutions for Zakharov system on
Nobu Kishimoto
Department of Mathematics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, JapanMasaya Maeda
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
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Abstract
We consider the Zakharov system in two space dimension with periodic boundary condition:
We prove the existence of finite time blow-up solutions of (Z). Further, we show there exists no minimal mass blow-up solution.
Résumé
Nous considérons le système de Zakharov dans lʼespace à deux dimensions avec la condition périodique au bord :
Nous prouvons lʼexistence de solutions de (Z) explosant au temps fini. En outre, nous prouvons quʼil nʼy a aucune solution explosive de masse minimale.
Cite this article
Nobu Kishimoto, Masaya Maeda, Construction of blow-up solutions for Zakharov system on . Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 5, pp. 791–824
DOI 10.1016/J.ANIHPC.2012.09.003