Exponential convergence for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise. (English) Zbl 1420.60088
Summary: The current paper is devoted to 3D stochastic Ginzburg-Landau equation with degenerate random forcing. We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure. To accomplish this, firstly we establish a type of gradient inequality, which is also essential to proving asymptotic strong Feller property. Then we prove that the corresponding dynamical system possesses a strong type of Lyapunov structure and is of a relatively weak form of irreducibility.
MSC:
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
37A25 | Ergodicity, mixing, rates of mixing |