Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations

Authors:
Jean Ginibre and Giorgio Velo

Journal:
Quart. Appl. Math. **68** (2010), 113-134

MSC (2000):
Primary 35P25; Secondary 35B40, 35Q40, 35Q55

DOI:
https://doi.org/10.1090/S0033-569X-09-01141-9

Published electronically:
October 26, 2009

MathSciNet review:
2598884

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Recently several authors have developed multilinear and in particular quadratic extensions of the classical Morawetz inequality. Those extensions provide (among other results) an easy proof of asymptotic completeness in the energy space for nonlinear Schrödinger equations in arbitrary space dimension and for Hartree equations in space dimension greater than two in the noncritical cases. We give a pedagogical review of the latter results.

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Additional Information

**Jean Ginibre**

Affiliation:
Laboratoire de Physique Théorique, Université de Paris XI, Bâtiment 210, F-91405 ORSAY Cedex, France

Email:
Jean.Ginibre@th.u-psud.fr

**Giorgio Velo**

Affiliation:
Dipartimento di Fisica, Università di Bologna and INFN, Sezione di Bologna, Italy

Email:
Velo@bo.infn.it

DOI:
https://doi.org/10.1090/S0033-569X-09-01141-9

Received by editor(s):
July 3, 2008

Received by editor(s) in revised form:
October 7, 2008

Published electronically:
October 26, 2009

Additional Notes:
First author’s sponsoring institution: Unité Mixte de Recherche (CNRS) UMR 8627

Dedicated:
Dedicated to Professor Walter Strauss on his 70th birthday

Article copyright:
© Copyright 2009
Brown University