Differential Equations Seminar
11 February 2020 @ 14:00 - 15:00
DECAY AND SCATTERING IN ENERGY SPACE FOR THE SOLUTION OF GENERALIZED HARTREE EQUATION
Abstract. We prove decay with respect some Lebesgue norms for a class of Schrödinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a straightforward product we obtain large-data scattering in the energy space for the solutions to the defocusing generalized Hartre equations with mass-energy intercritical nonlinearities in any space dimensions.