论文标题
玻尔兹曼方程的规律性符合宏观边界
Regularity for the Boltzmann equation conditional to macroscopic bounds
论文作者
论文摘要
Boltzmann方程是一种非线性偏微分方程，在统计力学中起着核心作用。从数学的角度来看，任意初始数据的全局平滑解决方案的存在是一个悬而未决的开放问题。在本文中，我们回顾了一项针对粒子相互作用类型的程序，称为非切割。它专门用于$ c^\ infty $的先验估计，仅取决于身体上有意义的条件。我们证明，只要其质量，能量和熵密度保持界限并远离真空，该溶液将保持均匀平滑。
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an outstanding open problem. In the present article, we review a program focused on the type of particle interactions known as non-cutoff. It is dedicated to the derivation of a priori estimates in $C^\infty$, depending only on physically meaningful conditions. We prove that the solution will stay uniformly smooth provided that its mass, energy and entropy densities remain bounded, and away from vacuum.
