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Two dimensional Gross-Pitaevskii equation with space-time white noise (2101.10106v2)
Published 25 Jan 2021 in math.PR and math.AP
Abstract: In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg-Landau equation with a harmonic potential and an additive space-time white noise. We study the well-posedness of the model using an inhomogeneous Wick renormalization due to the potential, and prove the existence of an invariant measure and of stationary martingale solutions.