Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

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
Published electronically: October 26, 2009
MathSciNet review: 2598884
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35P25, 35B40, 35Q40, 35Q55

Retrieve articles in all journals with MSC (2000): 35P25, 35B40, 35Q40, 35Q55


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: http://dx.doi.org/10.1090/S0033-569X-09-01141-9
PII: S 0033-569X(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



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2014 Brown University
Comments: qam-query@ams.org
AMS Website