Ergodicity of 2D stochastic Ginzburg–Landau–Newell equations driven by degenerate noise |
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Authors: | Tianlong Shen Jianhua Huang |
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Affiliation: | College of Science, National University of Defense Technology, Changsha, China |
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Abstract: | The current paper is devoted to stochastic Ginzburg–Landau–Newell equation with degenerate random forcing. The existence and pathwise uniqueness of strong solutions with H1‐initial data is established, and then the existence of an invariant measure for the Feller semigroup is shown by Krylov–Bogoliubov theorem. Because of the coupled items in the stochastic Ginzburg–Landau–Newell equations, the higher order momentum estimates can be only obtained in the L2‐norm. We show the ergodicity of invariant measure for the transition semigroup by asymptotically strong Feller property and the support property. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | stochastic Ginzburg– Landau– Newell equations ergodicity degenerate noise invariant measure asymptotically strong Feller property |
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