The Non-Linear Fokker–Planck Equation in Low-Regularity Space
We construct the global existence and exponential time decay rates of mild solutions to the non-linear Fokker–Planck equation near a global Maxwellians with small-amplitude initial data in the low regularity function space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML...
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1576 |
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| author | Yingzhe Fan Bo Tang |
| author_facet | Yingzhe Fan Bo Tang |
| author_sort | Yingzhe Fan |
| collection | DOAJ |
| description | We construct the global existence and exponential time decay rates of mild solutions to the non-linear Fokker–Planck equation near a global Maxwellians with small-amplitude initial data in the low regularity function space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>L</mi><mi>k</mi><mn>1</mn></msubsup><msubsup><mi>L</mi><mi>T</mi><mo>∞</mo></msubsup><msubsup><mi>L</mi><mi>v</mi><mn>2</mn></msubsup></mrow></semantics></math></inline-formula> where the regularity assumption on the initial data is weaker. |
| first_indexed | 2024-03-10T03:55:28Z |
| format | Article |
| id | doaj.art-46dfe3918d774f94ba50a5fe1f9c374b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:55:28Z |
| publishDate | 2022-05-01 |
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| series | Mathematics |
| spelling | doaj.art-46dfe3918d774f94ba50a5fe1f9c374b2023-11-23T08:46:24ZengMDPI AGMathematics2227-73902022-05-01109157610.3390/math10091576The Non-Linear Fokker–Planck Equation in Low-Regularity SpaceYingzhe Fan0Bo Tang1School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, ChinaSchool of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang 441053, ChinaWe construct the global existence and exponential time decay rates of mild solutions to the non-linear Fokker–Planck equation near a global Maxwellians with small-amplitude initial data in the low regularity function space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>L</mi><mi>k</mi><mn>1</mn></msubsup><msubsup><mi>L</mi><mi>T</mi><mo>∞</mo></msubsup><msubsup><mi>L</mi><mi>v</mi><mn>2</mn></msubsup></mrow></semantics></math></inline-formula> where the regularity assumption on the initial data is weaker.https://www.mdpi.com/2227-7390/10/9/1576non-linear Fokker–Planck equationglobal existenceexponential time decay rateslow regularity function space |
| spellingShingle | Yingzhe Fan Bo Tang The Non-Linear Fokker–Planck Equation in Low-Regularity Space Mathematics non-linear Fokker–Planck equation global existence exponential time decay rates low regularity function space |
| title | The Non-Linear Fokker–Planck Equation in Low-Regularity Space |
| title_full | The Non-Linear Fokker–Planck Equation in Low-Regularity Space |
| title_fullStr | The Non-Linear Fokker–Planck Equation in Low-Regularity Space |
| title_full_unstemmed | The Non-Linear Fokker–Planck Equation in Low-Regularity Space |
| title_short | The Non-Linear Fokker–Planck Equation in Low-Regularity Space |
| title_sort | non linear fokker planck equation in low regularity space |
| topic | non-linear Fokker–Planck equation global existence exponential time decay rates low regularity function space |
| url | https://www.mdpi.com/2227-7390/10/9/1576 |
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