Nonlinear Schrodinger equation with time dependent potential

TL;DR

This paper establishes global well-posedness for nonlinear Schrödinger equations with time-dependent potentials, focusing on harmonic potentials relevant to physics, and analyzes the growth of high Sobolev norms of solutions.

Contribution

It proves well-posedness for these equations and investigates the behavior of solutions under time-dependent harmonic potentials, linking mathematical analysis with physical applications.

Findings

Global well-posedness for the equations.

Analysis of high Sobolev norm growth.

Relevance to Bose-Einstein condensation and wave packet propagation.

Abstract

We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation), and appears also as a preparation for the analysis of the propagation of wave packets in a nonlinear context. The main aspect considered here is the growth of high Sobolev norms of the solution.