Bilinear virial identities and applications

Planchon, Fabrice; Vega, Luis

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 2, pp. 261-290.

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.

Classification : 35Q55
Keywords: nonlinear Schrödinger equation, Virial identity, exterior domain
Mot clés : Équation de Schrödinger non linéaire, identité du Viriel, domaine extérieur

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