Momentum estimates and ergodicity for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise |
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Authors: | Xueke Pu Boling Guo |
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Institution: | a College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China b Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China |
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Abstract: | In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H1-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup. |
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Keywords: | 60H15 37A25 35Q35 |
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