具有强阻尼的 Boussinesq 方程指数吸引子的存在性
Existence of Exponential Attractor with Strong Damping Boussinesq Equation
DOI: 10.12677/PM.2024.144105, PDF, 下载: 44  浏览: 71  国家自然科学基金支持
作者: 张梦琪：西北师范大学数学与统计学院，甘肃 兰州
关键词: Boussinesq 方程；算子分解；指数吸引子；Boussinesq Equation； Operator Decomposition； Exponential Attractors
摘要: 本文研究了带有强阻尼的 Boussinesq 方程指数吸引子的存在性。Boussinesq 方程作为一个重要模型，被广泛地应用于描述一些大气物理流，如大气中的流体和海洋中的流体遇到的湍流现象，并在天气预报、船舶海运等实际生活中也有着广泛的应用。 首先，在本文中运用能量估计的方法证明了空间 H−1(Ω) × H01(Ω) 和 L2(Ω) × (H2(Ω)∩H01(Ω)) 中有界吸收集的存在性；其次，通过算子分解的方法获得了该问题的指数吸引子的存在性。 作为额外的收获, 本文获得了全局吸引子具有有限的分形维数。
Abstract: In this paper, the existence of exponential attractors of Boussinesq equation with strong damping is studied. The Boussinesq equation, as an important model, has been widely used to describe some atmospheric physical flows, such as turbulence encountered by fluids in the atmosphere and fluids in the ocean, and has also been widely used in practical life such as weather forecasting and shipping. First of all, in this article, the existence of bounded absorption set in space H−1(Ω) × H01(Ω) and L2(Ω) × (H2(Ω)∩H01(Ω)) is proved by energy estimation method; Secondly, we obtain the existence of the exponential attractor by the method of operator decomposition. As a byproduction, we achieve that the global attractor has a finite fractal dimension.
文章引用：张梦琪. 具有强阻尼的 Boussinesq 方程指数吸引子的存在性[J]. 理论数学, 2024, 14(4): 1-17. https://doi.org/10.12677/PM.2024.144105

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