Global well-posedness and instability of an inhomogeneous nonlinear Schrodinger equation with harmonic potential

TL;DR

This paper investigates the global behavior and stability of solutions to an inhomogeneous nonlinear Schrödinger equation with exponential nonlinearity and harmonic potential in two dimensions, establishing well-posedness, ground states, and instability results.

Contribution

It provides the first analysis of global well-posedness and instability for this specific inhomogeneous Schrödinger equation with exponential growth in two dimensions.

Findings

Proved global well-posedness of the equation.

Established existence of ground states.

Demonstrated instability of standing waves.

Abstract

This paper is concerned with the Cauchy problem for an inhomogeneous nonlinear Schrodinger equation with exponential growth nonlinearity and harmonic potential in two space dimensions. We prove global well-posedness, existence of the associated ground state and instability of the standing wave.