RANDOM ATTRACTOR FOR FRACTIONAL GINZBURG-LANDAU EQUATION WITH MULTIPLICATIVE NOISE

Abstract

In this paper, we consider the asymptotic behavior of solutions to the stochastic fractional complex Ginzburg-Landau equation with multiplicative noise in one spatial dimensions. We first transfer stochastic fractional Ginzburg-Landau equation into random equation which solutions generate a random dynamical system. Then, we consider the existence of a random attractor for the random dynamical system. At last we estimate the Hausdorff dimension of the random attractor by using linearization and Lyapunov exponents.