Nous profilons une démonstration de l’existence globale et diffusion pour l’équation de Schrödinger nonlinéaire répulsive cubique avec données à pour . 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 for . The proof uses a new estimate of Morawetz type.
@article{JEDP_2002____A10_0, 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://www.numdam.org/articles/10.5802/jedp.608/} }
TY - JOUR AU - Colliander, J. AU - Keel, M. AU - Staffilani, G. AU - Takaoka, H. AU - Tao, T. TI - Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $mathbb{R}^3$ en dessous l’espace d’énergie JO - Journées équations aux dérivées partielles PY - 2002 SP - 1 EP - 15 PB - Université de Nantes UR - http://www.numdam.org/articles/10.5802/jedp.608/ DO - 10.5802/jedp.608 LA - en ID - JEDP_2002____A10_0 ER -
%0 Journal Article %A Colliander, J. %A Keel, M. %A Staffilani, G. %A Takaoka, H. %A Tao, T. %T Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur $mathbb{R}^3$ en dessous l’espace d’énergie %J Journées équations aux dérivées partielles %D 2002 %P 1-15 %I Université de Nantes %U http://www.numdam.org/articles/10.5802/jedp.608/ %R 10.5802/jedp.608 %G en %F JEDP_2002____A10_0
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://www.numdam.org/articles/10.5802/jedp.608/
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