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

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 \(L^{2}\) $L^2$ .