Stochastic complex Ginzburg-Landau equation on compact surfaces

Published 28 Feb 2025 in math.AP and math.PR | (2502.21128v1)

Abstract: We study a stochastic complex Ginzburg-Landau equation (SCGL) on compact surfaces with magnetic Laplacian and polynomial nonlinearity, forced by a space-time white noise. After renormalizing the equation in a suitable manner, we show that the dynamics is locally well-posed. Moreover, we prove deterministic global well-posedness for the defocusing SCGL in the weakly dispersive regime.

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