Construction of blow-up solutions for Zakharov system on 𝕋 2
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 5, pp. 791-824.

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.

DOI : 10.1016/j.anihpc.2012.09.003
Classification : 35Q55
Mots clés : Zakharov system, Blow-up solution, Modified energy, Minimal mass blow-up solution
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     title = {Construction of blow-up solutions for {Zakharov} system on $ {\mathbb{T}}^{2}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {791--824},
     publisher = {Elsevier},
     volume = {30},
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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) no. 5, pp. 791-824. doi : 10.1016/j.anihpc.2012.09.003. http://www.numdam.org/articles/10.1016/j.anihpc.2012.09.003/

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