PDE Seminar: Guo -- Global solutions to 3D quadratic nonlinear Schrodinger-type equation

Speaker: Professor Zihua Guo (Monash University) 

Date: Monday 7th July 2025, 11:00-12:00, Carslaw Room 535 

Title: Global solutions to 3D quadratic nonlinear Schrodinger-type equation 

Abstract: We consider the Cauchy problem to the 3D fractional Schrodinger equation with
quadratic interaction of uu¯ type.  We prove the global existence of solutions and
scattering properties for small initial data.  For the proof, one novelty is that we
combine the normal form methods and the space-time resonance methods.  Using the normal
form transform enables us more flexibilities in designing the resolution spaces so that
we can control various interactions.  It is also convenient for the final data problem.
This is a joint work with Naijia Liu and Liang Song.