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

Ginibre, Jean; Velo, Giorgio

doi:10.1090/S0033-569X-09-01141-9

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
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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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