Bilinear virial identities and applications

Abstract

We prove bilinear virial identities for the nonlinear Schrodinger 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.

30 pages, final version to appear in the Annales Scientifiques de l'ENS