Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces
We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type equation with a nonlocal velocity field, the so-called aggregati...
| Principais autores: | , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
Elsevier
2020
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| _version_ | 1826260429705314304 |
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| author | Carrillo de la Plata, JA Choi, YP |
| author_facet | Carrillo de la Plata, JA Choi, YP |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type equation with a nonlocal velocity field, the so-called aggregation equation, by employing 2-Wasserstein distance. By introducing an intermediate system, given by the pressureless Euler equations with nonlocal forces, we can quantify the error between the spatial densities of the kinetic equation and the pressureless Euler system by means of relative entropy type arguments combined with the 2-Wasserstein distance. This together with the quantitative error estimate between the pressureless Euler system and the aggregation equation in 2-Wasserstein distance in [Commun. Math. Phys, 365, (2019), 329–361] establishes the quantitative bounds on the error between the kinetic equation and the aggregation equation. |
| first_indexed | 2024-03-06T19:05:32Z |
| format | Journal article |
| id | oxford-uuid:14fc2d68-a19f-4ac5-9d75-2555d77f2d1c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:05:32Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:14fc2d68-a19f-4ac5-9d75-2555d77f2d1c2022-03-26T10:22:59ZQuantitative error estimates for the large friction limit of Vlasov equation with nonlocal forcesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:14fc2d68-a19f-4ac5-9d75-2555d77f2d1cEnglishSymplectic ElementsElsevier2020Carrillo de la Plata, JAChoi, YPWe study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type equation with a nonlocal velocity field, the so-called aggregation equation, by employing 2-Wasserstein distance. By introducing an intermediate system, given by the pressureless Euler equations with nonlocal forces, we can quantify the error between the spatial densities of the kinetic equation and the pressureless Euler system by means of relative entropy type arguments combined with the 2-Wasserstein distance. This together with the quantitative error estimate between the pressureless Euler system and the aggregation equation in 2-Wasserstein distance in [Commun. Math. Phys, 365, (2019), 329–361] establishes the quantitative bounds on the error between the kinetic equation and the aggregation equation. |
| spellingShingle | Carrillo de la Plata, JA Choi, YP Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title | Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title_full | Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title_fullStr | Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title_full_unstemmed | Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title_short | Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces |
| title_sort | quantitative error estimates for the large friction limit of vlasov equation with nonlocal forces |
| work_keys_str_mv | AT carrillodelaplataja quantitativeerrorestimatesforthelargefrictionlimitofvlasovequationwithnonlocalforces AT choiyp quantitativeerrorestimatesforthelargefrictionlimitofvlasovequationwithnonlocalforces |