Stability of the Stochastic Ginzburg–Landau–Newell Equations in Two Dimensions

Abstract

This paper concerns the 2D stochastic Ginzburg–Landau–Newell equations with a degenerate random forcing. We study the relationship between stationary distributions which correspond to the original and perturbed systems and then prove the stability of the stationary distribution. This suggests that the complexity of stochastic systems is likely to be robust. The main difficulty of the proof lies in estimating the expectation of exponential moments and controlling nonlinear terms while working on the evolution triple H2⊂H1⊂H0 to obtain a bound on the difference between the original solution and the perturbed solution.

Keywords

• stochastic stability
• stochastic Ginzburg–Landau–Newell equations
• stationary distribution
• exponential ergodicity