| 无界槽形区域上Boussinesq方程的整体吸引子 |
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| 引用本文： | 王学锋,杨德生.无界槽形区域上Boussinesq方程的整体吸引子[J].华东师范大学学报(自然科学版),2002(2):1-14. |
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| 作者姓名： | 王学锋 杨德生 |
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| 作者单位： | 1. 华东师范大学,数学系,上海,200062
2. 中南大学,数学系,长沙,410083 |
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| 基金项目： | 国家自然科学基金 (195 710 2 6 ) |
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| 摘 要： | 该文讨论了无界域上Boussinesq方程解的渐近行为，证明了在一定条件下，Boussinesq方程整体吸引子的存在笥及其整体吸引子具有有限的Hausdorff维数。作者将主要利用加权Sobolev空间的估计技巧讨论无界域上吸收集的紧性。
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| 关 键 词： | 整体吸引子 Boussinesq方程 加权Sobolev空间 Hausdorff维数 |
The Global Attractor of the Boussinesq Equations in an Unbounded Channel-like Domain |
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| WANG Xue feng ,YANG De sheng.The Global Attractor of the Boussinesq Equations in an Unbounded Channel-like Domain[J].Journal of East China Normal University(Natural Science),2002(2):1-14. |
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| Authors: | WANG Xue feng YANG De sheng |
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| Institution: | WANG Xue feng 1,YANG De sheng 2 |
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| Abstract: | Our discussion in this paper is about the asymptotic behavior of the solutions for the Boussinesq equations in an unbounded domain. It has already been proved that when an external force decays at infinity, the semigroup generated by the Boussinesq equations acquires a global attractor and the Housdorff dimension of the attrctor is finite. We shall propose some methods to prove the compactness of the absorbing set in unbounded domain. Estimates in weighted Sobolev spaces are used as a main tool. |
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| Keywords: | global attractor Boussinesq equations weighted Sobolev spaces Housdorff dimension |
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