论文标题
在融合到Fermi-Dirac颗粒的空间均匀玻尔兹曼方程的平衡上
On the convergence to equilibrium for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles
论文作者
论文摘要
在本文中，我们证明了FERMI-DIRAC颗粒的空间均匀玻尔兹曼方程的解决方案的溶液（一般初始数据）的均衡（具有一般初始数据）。碰撞内核的假设包括较弱的角截止的库仑电势。证明是基于力矩估计，熵耗散不平等，碰撞增益操作员的规律性以及许多新的观察结果，即许多碰撞内核大于或等于某些完全正面的内核，这使我们能够避免处理立方体碰撞积分的融合问题。
In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision kernel includes the Coulomb potential with a weaker angular cutoff. The proof is based on moment estimates, entropy dissipation inequalities, regularity of the collision gain operator, and a new observation that many collision kernels are larger than or equal to some completely positive kernels, which enables us to avoid dealing with the convergence problem of the cubic collision integrals.
