Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise

Abstract

In this work, we focus on the long-time behavior of the solutions of the stochastic fractional complex Ginzburg–Landau equation defined on Rn with polynomial drift terms of arbitrary order. The well-posedness of the equation based on pathwise uniform estimates and uniform estimates on average are proved. Following this, the existence and uniqueness of weak pullback random attractors are establsihed.

Keywords

• fractional complex Ginzburg–Landau equation
• mean random attractor
• nonlinear noise
• unbounded domain
• locally Lipschitz continuous