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

Elie Abdo; Quyuan Lin

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arXiv · 2409.05209

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

Elie Abdo·Quyuan Lin

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Abstract

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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Elie Abdo, Quyuan Lin. 2024-09-08. On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains. https://arxiv.org/abs/2409.05209

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