[Identités virielles bilinéaires et applications]
On démontre des identités de type viriel bilinéaire pour l'équation de Schrödinger nonlinéaire, qui peuvent être vues comme des extensions des inégalités d'interaction de Morawetz. Ceci permet de retrouver et d'étendre des raffinements bilinéaires des inégalités de Strichartz, et nous donnons également des applications à plusieurs problèmes non-linéaires, notamment sur les domaines à bord.
We prove bilinear virial identities for the nonlinear Schrödinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on domains with boundaries.
Keywords: nonlinear Schrödinger equation, Virial identity, exterior domain
Mot clés : Équation de Schrödinger non linéaire, identité du Viriel, domaine extérieur
@article{ASENS_2009_4_42_2_261_0, author = {Planchon, Fabrice and Vega, Luis}, title = {Bilinear virial identities and applications}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {261--290}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 42}, number = {2}, year = {2009}, doi = {10.24033/asens.2096}, mrnumber = {2518079}, zbl = {1192.35166}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.2096/} }
TY - JOUR AU - Planchon, Fabrice AU - Vega, Luis TI - Bilinear virial identities and applications JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 261 EP - 290 VL - 42 IS - 2 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/asens.2096/ DO - 10.24033/asens.2096 LA - en ID - ASENS_2009_4_42_2_261_0 ER -
%0 Journal Article %A Planchon, Fabrice %A Vega, Luis %T Bilinear virial identities and applications %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 261-290 %V 42 %N 2 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/asens.2096/ %R 10.24033/asens.2096 %G en %F ASENS_2009_4_42_2_261_0
Planchon, Fabrice; Vega, Luis. Bilinear virial identities and applications. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 2, pp. 261-290. doi : 10.24033/asens.2096. https://www.numdam.org/articles/10.24033/asens.2096/
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