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磁场作用下Vlasov-Euler-Fokker-Planck解的全局存在性和正则性
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Abstract:
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。
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.
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