Critical exponents line, scattering thoeries for a weighted gradient system of semilinear Schrodinger equations

TL;DR

This paper investigates the critical exponents and scattering behavior of solutions to a weighted gradient system of semilinear Schrödinger equations, establishing well-posedness and scattering theories in specific dimensions.

Contribution

It identifies a critical exponents line in 3D and a critical point in 4D, and develops scattering theories for global solutions of the system.

Findings

Existence of a critical exponents line in 3D

Existence of a critical exponents point in 4D

Development of scattering theories for global solutions

Abstract

We establish the local wellposedness of different type of solutions the system with different types of initial data. We find there exists a critical exponents line in space dimension 3 and critical exponents point in space dimension 4. We also establish different scattering theories for the global solutions.