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.
Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schroedinger and Hartree equations / J.Ginibre; G.Velo. - In: QUARTERLY OF APPLIED MATHEMATICS. - ISSN 0033-569X. - STAMPA. - 68:(2010), pp. 113-134. [10.1090/S0033-569X-09-01141-9]
Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schroedinger and Hartree equations
VELO, GIORGIO
2010
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
