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

Elie Abdo; Quyuan Lin

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

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arxiv 2409.05209 v1 pith:XZ6EWXFS submitted 2024-09-08 math.AP

Elie Abdo , Quyuan Lin This is my paper · ORCID

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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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