Global solutions to a nonlinear Fokker-Planck equation
In this paper, we construct global solutions to the Cauchy problem on a nonlinear Fokker-Planck equation near Maxwellian with small-amplitude initial data in Sobolev space $ H^2_{x}L^2_v $ by a refined nonlinear energy method. Compared with the results of Liao et al. (Global existence and decay rate...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023822?viewType=HTML |
| _version_ | 1797822564026810368 |
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| author | Xingang Zhang Zhe Liu Ling Ding Bo Tang |
| author_facet | Xingang Zhang Zhe Liu Ling Ding Bo Tang |
| author_sort | Xingang Zhang |
| collection | DOAJ |
| description | In this paper, we construct global solutions to the Cauchy problem on a nonlinear Fokker-Planck equation near Maxwellian with small-amplitude initial data in Sobolev space $ H^2_{x}L^2_v $ by a refined nonlinear energy method. Compared with the results of Liao et al. (Global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations, <italic>J. Stat. Phys.</italic>, <bold>173</bold> (2018), 222–241.), the regularity assumption on the initial data is much weaker. |
| first_indexed | 2024-03-13T10:10:57Z |
| format | Article |
| id | doaj.art-d4671e182f914e96a1aac20baa36d9cc |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T10:10:57Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-d4671e182f914e96a1aac20baa36d9cc2023-05-22T01:06:39ZengAIMS PressAIMS Mathematics2473-69882023-05-0187161151612610.3934/math.2023822Global solutions to a nonlinear Fokker-Planck equationXingang Zhang0Zhe Liu 1Ling Ding 2Bo Tang 31. School of Computer Science and Technology, Nanyang Normal University, Nanyang, Henan 473061, China2. Nanyang Normal University, Nanyang, Henan 473061, China3. School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China3. School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China 4. Hubei Key Laboratory of Power System Design and Test for Electrical Vehicle, Hubei University of Arts and Science, Xiangyang, Hubei 441053, ChinaIn this paper, we construct global solutions to the Cauchy problem on a nonlinear Fokker-Planck equation near Maxwellian with small-amplitude initial data in Sobolev space $ H^2_{x}L^2_v $ by a refined nonlinear energy method. Compared with the results of Liao et al. (Global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations, <italic>J. Stat. Phys.</italic>, <bold>173</bold> (2018), 222–241.), the regularity assumption on the initial data is much weaker. https://www.aimspress.com/article/doi/10.3934/math.2023822?viewType=HTMLnonlinear fokker-planck equationglobal existenceenergy methodcauchy problempriori estimates |
| spellingShingle | Xingang Zhang Zhe Liu Ling Ding Bo Tang Global solutions to a nonlinear Fokker-Planck equation AIMS Mathematics nonlinear fokker-planck equation global existence energy method cauchy problem priori estimates |
| title | Global solutions to a nonlinear Fokker-Planck equation |
| title_full | Global solutions to a nonlinear Fokker-Planck equation |
| title_fullStr | Global solutions to a nonlinear Fokker-Planck equation |
| title_full_unstemmed | Global solutions to a nonlinear Fokker-Planck equation |
| title_short | Global solutions to a nonlinear Fokker-Planck equation |
| title_sort | global solutions to a nonlinear fokker planck equation |
| topic | nonlinear fokker-planck equation global existence energy method cauchy problem priori estimates |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023822?viewType=HTML |
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