A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916320319111168 |
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| author | Henderson, Christopher Lucertini, Giacomo Wang, Weinan |
| author_facet | Henderson, Christopher Lucertini, Giacomo Wang, Weinan |
| contents | In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation Henderson, Christopher Lucertini, Giacomo Wang, Weinan Analysis of PDEs 35Q84, 35K65, 26D10, 35A23 In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set. |
| title | A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation |
| topic | Analysis of PDEs 35Q84, 35K65, 26D10, 35A23 |
| url | https://arxiv.org/abs/2407.08785 |