Global solutions to 3D quadratic nonlinear Schrödinger-type equation

Dr. Naijia Liu
2025-11-27 10:00-11:00
MCM110

Speaker: Dr. Naijia Liu (Sun Yat-sen University)
Time: 
10:00-11:00  November 27th, 2025 (Thursday)

Place: MCM110

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

Abstract: We consider the Cauchy problem to the 3D fractional Schr\"odinger equation with quadratic interaction of $u\bar u$ 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 to have more flexibility in designing the resolution spaces so that we can control various interactions. It is also convenient for the final data problem.