Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations
In this paper, the existence and uniqueness of the global smooth solution to an initial-boundary value problem of one-dimensional magnetohydrodynamics (MHD)–Vlasov equations are proved for large initial data. This equation is a fluid-particle system which consists of the compressible MHD equations f...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/jofs/5526332 |
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| _version_ | 1850135366184468480 |
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| author | Peng Jiang Enqi Lin Lu Zhu |
| author_facet | Peng Jiang Enqi Lin Lu Zhu |
| author_sort | Peng Jiang |
| collection | DOAJ |
| description | In this paper, the existence and uniqueness of the global smooth solution to an initial-boundary value problem of one-dimensional magnetohydrodynamics (MHD)–Vlasov equations are proved for large initial data. This equation is a fluid-particle system which consists of the compressible MHD equations for the fluid coupled with the Vlasov equation for the particles through a nonlinear drag force. The proof relies on the local existence together with the uniform a priori estimates of solutions. In particular, in order to get a higher derivative estimate of the solution, we need to show the density distribution function of particle has compact support, which is obtained from the reflection boundary conditions of the particles combined with the characteristic curves method. |
| format | Article |
| id | doaj-art-e4b40b25eec047de876423f33b9885fb |
| institution | OA Journals |
| issn | 2314-8888 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e4b40b25eec047de876423f33b9885fb2025-08-20T02:31:27ZengWileyJournal of Function Spaces2314-88882025-01-01202510.1155/jofs/5526332Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov EquationsPeng Jiang0Enqi Lin1Lu Zhu2School of MathematicsSchool of MathematicsSchool of MathematicsIn this paper, the existence and uniqueness of the global smooth solution to an initial-boundary value problem of one-dimensional magnetohydrodynamics (MHD)–Vlasov equations are proved for large initial data. This equation is a fluid-particle system which consists of the compressible MHD equations for the fluid coupled with the Vlasov equation for the particles through a nonlinear drag force. The proof relies on the local existence together with the uniform a priori estimates of solutions. In particular, in order to get a higher derivative estimate of the solution, we need to show the density distribution function of particle has compact support, which is obtained from the reflection boundary conditions of the particles combined with the characteristic curves method.http://dx.doi.org/10.1155/jofs/5526332 |
| spellingShingle | Peng Jiang Enqi Lin Lu Zhu Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations Journal of Function Spaces |
| title | Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations |
| title_full | Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations |
| title_fullStr | Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations |
| title_full_unstemmed | Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations |
| title_short | Global Existence of Smooth Solutions to an Initial-Boundary Value Problem of One-Dimensional MHD–Vlasov Equations |
| title_sort | global existence of smooth solutions to an initial boundary value problem of one dimensional mhd vlasov equations |
| url | http://dx.doi.org/10.1155/jofs/5526332 |
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