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

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.

101 Pages

References in corpus (1)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

Cited by in corpus (1)

• $H_x^s\times H_x^s$ scattering theory for a weighted gradient system of 3D radial defocusing NLS