Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
Published 2017-08-07Version 1
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise. Two important questions for this system are the global existence of solutions in the support of the Gibbs measure, and the convergence of those solutions to the equilibrium for large time. In this paper, we give a proof of these two results in one space dimension. In order to prove the convergence to equilibrium, we use the associated purely dissipative equation as an auxiliary equation, for which the convergence may be obtained using standard techniques.
Flat blow-up solutions for the complex Ginzburg Landau equation
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Convergence of the regularized short pulse equation to the short pulse one
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