H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions
This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/706091 |
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| author | Yijin Zhang |
| author_facet | Yijin Zhang |
| author_sort | Yijin Zhang |
| collection | DOAJ |
| description | This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system. |
| format | Article |
| id | doaj-art-cbd69104f19c47baa2029224fdf485e8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cbd69104f19c47baa2029224fdf485e82025-02-03T01:21:36ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/706091706091H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary ConditionsYijin Zhang0School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThis work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system.http://dx.doi.org/10.1155/2013/706091 |
| spellingShingle | Yijin Zhang H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions Abstract and Applied Analysis |
| title | H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions |
| title_full | H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions |
| title_fullStr | H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions |
| title_full_unstemmed | H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions |
| title_short | H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions |
| title_sort | h1 random attractors and asymptotic smoothing effect of solutions for stochastic boussinesq equations with fluctuating dynamical boundary conditions |
| url | http://dx.doi.org/10.1155/2013/706091 |
| work_keys_str_mv | AT yijinzhang h1randomattractorsandasymptoticsmoothingeffectofsolutionsforstochasticboussinesqequationswithfluctuatingdynamicalboundaryconditions |