Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system
We provide a quantitative asymptotic analysis for the nonlinear Vlasov–Poisson–Fokker–Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a we...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Institute of Mathematical Sciences
2021
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| _version_ | 1797107004662087680 |
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| author | Carrillo, JA Choi, Y-P Peng, Y |
| author_facet | Carrillo, JA Choi, Y-P Peng, Y |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | We provide a quantitative asymptotic analysis for the nonlinear Vlasov–Poisson–Fokker–Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov–Poisson–Fokker–Planck system strongly converges to a strong solution to the diffusive model. Our proof relies on the modulated macroscopic kinetic energy estimate based on the weak-strong uniqueness principle together with a careful analysis of the Poisson equation. |
| first_indexed | 2024-03-07T07:10:29Z |
| format | Journal article |
| id | oxford-uuid:3c96571d-4905-4ae5-b59d-da4bce1a8671 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:10:29Z |
| publishDate | 2021 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:3c96571d-4905-4ae5-b59d-da4bce1a86712022-06-22T15:56:47ZLarge friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck systemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3c96571d-4905-4ae5-b59d-da4bce1a8671EnglishSymplectic ElementsAmerican Institute of Mathematical Sciences2021Carrillo, JAChoi, Y-PPeng, YWe provide a quantitative asymptotic analysis for the nonlinear Vlasov–Poisson–Fokker–Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov–Poisson–Fokker–Planck system strongly converges to a strong solution to the diffusive model. Our proof relies on the modulated macroscopic kinetic energy estimate based on the weak-strong uniqueness principle together with a careful analysis of the Poisson equation. |
| spellingShingle | Carrillo, JA Choi, Y-P Peng, Y Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title | Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title_full | Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title_fullStr | Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title_full_unstemmed | Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title_short | Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system |
| title_sort | large friction high force fields limit for the nonlinear vlasov poisson fokker planck system |
| work_keys_str_mv | AT carrilloja largefrictionhighforcefieldslimitforthenonlinearvlasovpoissonfokkerplancksystem AT choiyp largefrictionhighforcefieldslimitforthenonlinearvlasovpoissonfokkerplancksystem AT pengy largefrictionhighforcefieldslimitforthenonlinearvlasovpoissonfokkerplancksystem |