Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces
In this paper, we are concerned with the local well-posedness of the Vlasov-Poisson-Fokker-Planck equation near vacuum in the fractional Sobolev-Lebesgue space for the large initial data. To achieve this goal, we mainly adopt the energy method. In order to obtain the energy estimate, we establish an...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Mathyze Publishers
2022-12-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/83 |
| _version_ | 1797388588887834624 |
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| author | Jingchun Chen Cong He |
| author_facet | Jingchun Chen Cong He |
| author_sort | Jingchun Chen |
| collection | DOAJ |
| description | In this paper, we are concerned with the local well-posedness of the Vlasov-Poisson-Fokker-Planck equation near vacuum in the fractional Sobolev-Lebesgue space for the large initial data. To achieve this goal, we mainly adopt the energy method. In order to obtain the energy estimate, we establish an L2-Lq estimate related to the electronic term, and take advantage of the commutator estimates as well. |
| first_indexed | 2024-03-08T22:42:56Z |
| format | Article |
| id | doaj.art-088a9fc1f0ba40a88401c48f7dbd2211 |
| institution | Directory Open Access Journal |
| issn | 2832-4293 |
| language | English |
| last_indexed | 2024-03-08T22:42:56Z |
| publishDate | 2022-12-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj.art-088a9fc1f0ba40a88401c48f7dbd22112023-12-17T09:16:13ZengMathyze PublishersPan-American Journal of Mathematics2832-42932022-12-011010.28919/cpr-pajm/1-1717Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue SpacesJingchun ChenCong HeIn this paper, we are concerned with the local well-posedness of the Vlasov-Poisson-Fokker-Planck equation near vacuum in the fractional Sobolev-Lebesgue space for the large initial data. To achieve this goal, we mainly adopt the energy method. In order to obtain the energy estimate, we establish an L2-Lq estimate related to the electronic term, and take advantage of the commutator estimates as well.https://mathyze.com/index.php/pajm/article/view/83 |
| spellingShingle | Jingchun Chen Cong He Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces Pan-American Journal of Mathematics |
| title | Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces |
| title_full | Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces |
| title_fullStr | Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces |
| title_full_unstemmed | Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces |
| title_short | Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces |
| title_sort | vlasov poisson fokker planck in fractional sobolev lebesgue spaces |
| url | https://mathyze.com/index.php/pajm/article/view/83 |
| work_keys_str_mv | AT jingchunchen vlasovpoissonfokkerplanckinfractionalsobolevlebesguespaces AT conghe vlasovpoissonfokkerplanckinfractionalsobolevlebesguespaces |