Global Existence of Smooth Solutions to an Initial‐Boundary Value Problem of One‐Dimensional MHD–Vlasov Equations

• Published in: Journal of function spaces Vol. 2025; no. 1
• Main Authors: Jiang, Peng, Lin, Enqi, Zhu, Lu
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.01.2025; Wiley
• Subjects: Boundary conditions; Boundary value problems; Compressibility; Density distribution; Distribution functions; Drag; Estimates; Fluid dynamics; Magnetic fields; Magnetohydrodynamics; Velocity; Vlasov equations
• ISSN: 2314-8896; 2314-8888
• DOI: 10.1155/jofs/5526332

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.