关于迪里夏特分数拉普拉奇及其在有界域 SQG 方程中的应用

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-08 DOI:arxiv-2409.05209

Elie Abdo, Quyuan Lin

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引用次数: 0

摘要

我们研究了光滑边界域上分数 Dirichlet Laplacian 的新特性，并建立了分数乘积估计和非线性 Poincar\'e 不等式。我们还利用这些工具研究了在物理边界存在的情况下，受给定时间无关的体力作用的表面准地心吸力方程的长时间动力学，并证明了有限维全局吸引子的存在。

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On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains

We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincar\'e inequalities. We also use these tools to study the long-time dynamics of the surface quasi-geostrophic equation forced by some given time-independent body forces in the presence of physical boundaries and prove the existence of a finite-dimensional global attractor.

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arXiv - MATH - Analysis of PDEs

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