On the Nonlinear Schrodinger systems with local and nonlocal nolinearities Part1

TL;DR

This paper investigates the well-posedness of nonlinear Schrödinger systems with both local and nonlocal nonlinearities, considering magnetic fields, and establishes conditions for the existence of solutions.

Contribution

It introduces a comprehensive analysis of well-posedness for Schrödinger systems with combined local and nonlocal nonlinearities in the presence of magnetic fields.

Findings

Established local and global well-posedness conditions

Proved existence of solutions under various physical assumptions

Extended analysis to systems with magnetic fields

Abstract

We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities.