SEMINARIO DI ANALISI ARMONICA

giovedì 22 novembre 2007

ore 11.00

Scuola Normale Superiore

Pisa

(Aula Tonelli)

Vittoria Pierfelice

Université de Orléans

Terrà  un seminario dal titolo:

“Global wellposedness and scattering results for nonlinear  Schrödinger equations on

 hyperbolic spaces”

Abstract

We study the dispersive properties of the Schrödinger equation on hyperbolic spaces, obtaining Strichartz estimates for a broader family of admissible pairs of exponents.

As a first consequence, we obtain considerably stronger wellposedness results for NLS. A second important application of our global Strichartz  estimates  is to prove scattering for NLS both in L² and in H¹, without any assumption of symmetry or gauge invariance. Notice that, in the euclidean case, this is only possible for the critical power 1+4/n and can be false for  subcritical powers, while on the hyperbolic space global existence and scattering of  small L² solutions holds for all  powers strictly between 1 and 1+4/n. This is a direct effect of the negative curvature

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