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

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

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

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

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

Abstract
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.

DOI: 10.5802/jedp.608

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     author = {J. Colliander and M. Keel and G. Staffilani and H. Takaoka and T. Tao},
     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},
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     series = {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 = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.608/}
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J. Colliander; M. Keel; G. Staffilani; H. Takaoka; T. Tao. 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. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.608/

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