Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $mathbb{R}^3$ en dessous l’espace d’énergie

Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T.

doi:10.5802/jedp.608

Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur

m a t h b b R^{3}

en dessous l’espace d’énergie

Colliander, J. ; Keel, M. ; Staffilani, G. ; Takaoka, H. ; Tao, T.

Journées équations aux dérivées partielles (2002), article no. 10, 15 p.

Résumé
Abstract

Nous profilons une démonstration de l’existence globale et diffusion pour l’équation de Schrödinger nonlinéaire répulsive cubique avec données à $H^{s} (ℝ^{3})$ pour $s > \frac{4}{5}$ . Le raisonnement utilise une estimation nouvelle de type de Morawetz. Nous détaillerons la démonstration ailleurs.

We sketch a proof of global existence and scattering for the defocusing cubic nonlinear Schrödinger equation in $H^{s} (ℝ^{3})$ for $s > \frac{4}{5}$ . The proof uses a new estimate of Morawetz type.

DOI : 10.5802/jedp.608

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     author = {Colliander, J. and Keel, M. and Staffilani, G. and Takaoka, H. and Tao, T.},
     title = {Existence globale et diffusion pour l{\textquoteright}\'equation de {Schr\"odinger} non lin\'eaire r\'epulsive cubique sur $mathbb{R}^3$ en dessous l{\textquoteright}espace d{\textquoteright}\'energie},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {10},
     pages = {1--15},
     publisher = {Universit\'e de Nantes},
     year = {2002},
     doi = {10.5802/jedp.608},
     mrnumber = {1968206},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jedp.608/}
}

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Colliander, J.; Keel, M.; Staffilani, G.; Takaoka, H.; Tao, T. Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $mathbb{R}^3$ en dessous l’espace d’énergie. Journées équations aux dérivées partielles (2002), article  no. 10, 15 p. doi : 10.5802/jedp.608. http://archive.numdam.org/articles/10.5802/jedp.608/

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