Séminaire Physique mathématique ICJ

Resolvents and time decay estimates for dispersive equations on manifolds

by Viviana Grasselli (Universite Lorraine)

Fokko du Cloux (Bâtiment Braconnier)

Fokko du Cloux

Bâtiment Braconnier

We consider solutions of three models of dispersive equations: the Schrödinger, wave and Klein-Gordon equations. We prove time decay estimates for the local energy of these solutions on manifolds, giving optimal rates of decay. The properties of the evolution equations are derived by a spectral analysis of the resolvent of the Schrödinger operator. To study the resolvent and control its blowup when we get close to the spectrum we will apply Mourre theory and we will point out the main difficulties of this approach in the manifold case.


Johannes Kellendonk