发表机构
Yonsei University; Sangmyung University（延世大学; 祥明大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Fermi-Dirac BGK方程在Pauli容许初值下全局温和解的存在性，并通过矩相容正则化保持物理约束，进一步在一致矩和熵界下建立半经典极限，使量子解强收敛到经典BGK解。
AI 中文摘要
我们证明了空间非齐次Fermi-Dirac BGK方程对于具有有限质量和动能、满足Pauli容许条件的任意大小初值存在全局温和解，允许真空和局部饱和零温状态。该构造依赖于局部平衡的矩相容正则化，该正则化保持Pauli界和一致矩控制，同时在饱和边界处保持一致。解满足质量、动量和能量守恒，并且在额外的有限空间二阶矩假设下，满足整个Pauli区间上的熵间隙H定理。在一致矩和熵界条件下，我们进一步证明，在提取子序列后，量子温和解在相空间中强收敛，在有界时间区间上一致收敛到经典BGK方程的温和解。
英文摘要
We prove global existence of mild solutions to the spatially inhomogeneous Fermi--Dirac BGK equation for arbitrary-size Pauli-admissible initial data with finite mass and kinetic energy, allowing both vacuum and locally saturated zero-temperature states. The construction relies on a moment-compatible regularization of the local equilibrium that preserves the Pauli bound and uniform moment control while remaining consistent up to the saturation boundary. The solutions satisfy mass, momentum, and energy conservation and, under an additional finite spatial second-moment assumption, an entropy-gap H-theorem on the full Pauli interval. Under uniform moment and entropy bounds, we further prove that, after extraction of a subsequence, quantum mild solutions converge strongly in phase space, uniformly on bounded time intervals, to a mild solution of the classical BGK equation.
