On the Well-Posedness of Two Driven-Damped Gross Pitaevskii-Type Models for Exciton-Polariton Condensates

TL;DR

This paper investigates the mathematical well-posedness of two models describing the non-equilibrium behavior of exciton-polariton condensates, establishing local and global solutions for rough and square-integrable initial data.

Contribution

It provides the first local and global well-posedness results for these specific driven-damped Gross-Pitaevskii models using Fourier restriction techniques.

Findings

Established local well-posedness for rough initial data.

Extended results to global well-posedness for initial data in L^2.

Applied Bourgain's Fourier restriction method to these models.

Abstract

We study the well-posedness of two systems modeling the non-equilibrium dynamics of pumped decaying Bose-Einstein condensates. In particular, we present the local theory for rough initial data using the Fourier restricted norm method introduced by Bourgain. We extend the result globally for initial data in $L^2$.