Construction of blow-up solutions for Zakharov system on 𝕋 2
Kishimoto, Nobu ; Maeda, Masaya
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 791-824 / Harvested from Numdam

Nous considérons le système de Zakharov dans lʼespace à deux dimensions avec la condition périodique au bord : {i t u=-Δu+nu, tt n=Δn+Δ|u| 2 ,(t,x)[0,T)×𝕋 2 .(Z) Nous prouvons lʼexistence de solutions de (Z) explosant au temps fini. En outre, nous prouvons quʼil nʼy a aucune solution explosive de masse minimale.

We consider the Zakharov system in two space dimension with periodic boundary condition: {i t u=-Δu+nu, tt n=Δn+Δ|u| 2 ,(t,x)[0,T)×𝕋 2 .(Z) We prove the existence of finite time blow-up solutions of (Z). Further, we show there exists no minimal mass blow-up solution.

Publié le : 2013-01-01
DOI : https://doi.org/10.1016/j.anihpc.2012.09.003
Classification:  35Q55
@article{AIHPC_2013__30_5_791_0,
     author = {Kishimoto, Nobu and Maeda, Masaya},
     title = {Construction of blow-up solutions for Zakharov system on $ {\mathbb{T}}^{2}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {30},
     year = {2013},
     pages = {791-824},
     doi = {10.1016/j.anihpc.2012.09.003},
     mrnumber = {3103171},
     zbl = {06295442},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2013__30_5_791_0}
}
Kishimoto, Nobu; Maeda, Masaya. Construction of blow-up solutions for Zakharov system on $ {\mathbb{T}}^{2}$. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) pp. 791-824. doi : 10.1016/j.anihpc.2012.09.003. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_5_791_0/

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