Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn

Abstract

This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method.