The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge
In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a d...
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2025-01-01
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| author | Xianghong Hu Xianwen Zhang |
| author_facet | Xianghong Hu Xianwen Zhang |
| author_sort | Xianghong Hu |
| collection | DOAJ |
| description | In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a defect measure, which extends the results of Miot to the case of the Vlasov–Yukawa system. And compared with the Miot’s work, an important improvement is that our results do not require compact support conditions for spatial variables or uniform bound conditions for second-order spatial moments. In addition, the extra small condition for initial data is also not required. |
| format | Article |
| id | doaj-art-c7ba9b6df5f4419d93e6b791a9bbc67e |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-c7ba9b6df5f4419d93e6b791a9bbc67e2025-01-24T13:40:10ZengMDPI AGMathematics2227-73902025-01-0113232010.3390/math13020320The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point ChargeXianghong Hu0Xianwen Zhang1School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaIn this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a defect measure, which extends the results of Miot to the case of the Vlasov–Yukawa system. And compared with the Miot’s work, an important improvement is that our results do not require compact support conditions for spatial variables or uniform bound conditions for second-order spatial moments. In addition, the extra small condition for initial data is also not required.https://www.mdpi.com/2227-7390/13/2/320the Vlasov–Yukawa systemlarge datagyrokinetic limitEuler equationdefect measure |
| spellingShingle | Xianghong Hu Xianwen Zhang The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge Mathematics the Vlasov–Yukawa system large data gyrokinetic limit Euler equation defect measure |
| title | The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge |
| title_full | The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge |
| title_fullStr | The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge |
| title_full_unstemmed | The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge |
| title_short | The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge |
| title_sort | gyrokinetic limit for the two dimensional vlasov yukawa system with a point charge |
| topic | the Vlasov–Yukawa system large data gyrokinetic limit Euler equation defect measure |
| url | https://www.mdpi.com/2227-7390/13/2/320 |
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