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.

Abstract (VO)
Résumé

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.

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.

MR

DOI : 10.5802/jedp.608

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     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},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {10},
     pages = {1--15},
     year = {2002},
     publisher = {Universit\'e de Nantes},
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     language = {en},
     url = {https://www.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

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