Graduate Student Seminar- Scattering in generalized Hartree equation

Title: Scattering in generalized Hartree equation
Speaker: Anudeep Kumar
Date and Time: Monday, April 30, 2:30-3:30pm
Place: Rome 204
AbstractWe consider the focusing generalized Hartree equation in the mass-supercritical and energy-subcritical setting. The characterization of solutions behavior under the so called mass-energy threshold is known for the NLS case from the works of Holmer and Roudenko (radial) and Duyckaerts, Holmer and Roudenko (nonradial) and generalizations (Guevara and others). The scattering behavior is typically proved following the road map developed by Kenig and Merle in 2006, using the concentration compactness and rigidity properties, which is a standard tool by now in the dispersive problems.
In this work we give an alternative proof of scattering in the Hartree case, following the approach of Dodson and Murphy for the focusing 3d cubic NLS equation, which relies on the scattering criterion of Tao, combined with the radial Sobolev and Morawetz-type estimates.