磁化哈密顿动力学的超临界平均场极限
Supercritical mean--field limit for magnetized Hamiltonian dynamic
- The University of Texas at Austin（德克萨斯大学奥斯汀分校）
- University of Oxford（牛津大学）
- Beijing Normal University（北京师范大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对无碰撞等离子体的磁化弗拉索夫-泊松方程及相关库仑粒子系统，建立了二维带时变非均匀外磁场的超临界平均场与准中性极限，推导了闭合涡度形式并证明了极限系统的整体适定性。
AI中文摘要：
磁化弗拉索夫-泊松方程是无碰撞等离子体的基础动力学模型。我们在空间非均匀且随时间变化的外磁场存在下，建立了其二维准中性极限；在相同设定下，还建立了相关排斥库仑粒子系统的平均场与准中性组合极限，从而扩展了\cite{han2021newton}的结果。两种极限均导出带洛伦兹力的不可压缩欧拉方程。洛伦兹算子的逐点斜对称性是关键结构特征，其在调制能量估计中产生精确抵消，对控制极限动力学至关重要。我们进一步推导了闭合涡度形式，其中流体涡度与磁场的和随流输运，并耦合到空间平均速度的演化方程；最终建立了所得极限系统在利普希茨类中的整体适定性。
英文摘要：
The magnetized Vlasov--Poisson equation is a fundamental kinetic model for collisionless plasmas. We establish its quasi-neutral limit in two dimensions in the presence of a spatially inhomogeneous and time-dependent external magnetic field. In the same setting, we also establish the combined mean-field and quasi-neutral limit of the associated repulsive Coulomb particle system, thereby extending the results of \cite{han2021newton}. Both limits lead to the incompressible Euler equations with Lorentz forcing. A key structural feature is the pointwise skew-symmetry of the Lorentz operator, which produces exact cancellations in the modulated-energy estimates and is crucial for controlling the limiting dynamics. We further derive a closed vorticity formulation in which the sum of the fluid vorticity and the magnetic field is transported by the flow, coupled to an evolution equation for the spatial mean velocity. Finally, we establish global well-posedness of the resulting limiting system in the Lipschitz class.
