How to construct decay rates for kinetic Fokker--Planck equations?
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866917061821726720 |
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| author | Brigati, Giovanni Stoltz, Gabriel |
| author_facet | Brigati, Giovanni Stoltz, Gabriel |
| contents | We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions--Poincaré inequality and an averaging lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | How to construct decay rates for kinetic Fokker--Planck equations? Brigati, Giovanni Stoltz, Gabriel Analysis of PDEs Functional Analysis We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions--Poincaré inequality and an averaging lemma. |
| title | How to construct decay rates for kinetic Fokker--Planck equations? |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2302.14506 |