The mass-critical fourth-order Schrodinger equation in high dimensions

TL;DR

This paper establishes global well-posedness and scattering results for the mass-critical fourth-order Schrödinger equation in high dimensions, extending understanding of its behavior for both defocusing and focusing cases with general initial data.

Contribution

It provides the first comprehensive analysis of global solutions for the mass-critical fourth-order Schrödinger equation in high dimensions, including both defocusing and focusing scenarios.

Findings

Global well-posedness in high dimensions for defocusing case

Scattering results for initial data with mass below a threshold in focusing case

Extension of known results to fourth-order Schrödinger equations

Abstract

We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-order Schrodinger equation in high dimensions n>4, for general L^2 initial data in the defocusing case, and for general initial data with Mass less than certain fraction of the Mass of the Ground State in the focusing case.