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

References in corpus (1)

• Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $\mathbb{R}$

Cited by in corpus (5)

• On the decay of solutions to a class of defocusing NLS
• Scattering for the nonlinear Schrodinger equation with a general one-dimensional confinement
• Energy Critical NLS in two space dimensions
• Asymptotically linear solutions in H^1 of the 2-d defocusing nonlinear Schroedinger and Hartree equations
• Remarks on global a priori estimates for the nonlinear Schrödinger equation