磁场作用下Vlasov-Euler-Fokker-Planck解的全局存在性和正则性
Global Existence and Regularity of Vlasov-Euler-Fokker-Planck Solution with Magnetic Field
DOI: 10.12677/AAM.2023.124182, PDF,   
作者: 宋颍聪：上海理工大学理学院，上海
关键词: 不可压；经典解；正则性；能量估计；Incompressible； Classical Solution； Regularity； Energy Estimation
摘要: 本文研究了磁场作用下不可压缩Euler方程与Vlasov-Fokker-Planck方程通过斯托克斯阻力耦合而成的偏微分方程组系统。得到了接近平衡状态时经典解的整体时间存在性、正则性，并且得到了此系统具有瞬时的平滑效果。证明方法采用能量估计。
Abstract: In this paper, we consider the partial differential equation system of the incompressible Euler equation and the Vlasov-Fokker-Planck equation coupled by Stokes drag force. The global existence and regularity of classical solutions near equilibrium are obtained and we get the system has an in-stantaneous smoothing effect. Energy estimation is used to prove the method.
文章引用：宋颍聪. 磁场作用下Vlasov-Euler-Fokker-Planck解的全局存在性和正则性[J]. 应用数学进展, 2023, 12(4): 1753-1761. https://doi.org/10.12677/AAM.2023.124182

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