On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912018916704256 |
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| author | Abdo, Elie Lin, Quyuan |
| author_facet | Abdo, Elie Lin, Quyuan |
| contents | We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincaré 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains Abdo, Elie Lin, Quyuan Analysis of PDEs We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincaré 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. |
| title | On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.05209 |