Bilinear virial identities and applications. (English) Zbl 1192.35166
Authors’ abstract: 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.
Reviewer: Ma Wen-Xiu (Tampa)
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35P25 | Scattering theory for PDEs |
35J10 | Schrödinger operator, Schrödinger equation |
35B45 | A priori estimates in context of PDEs |