标题： 玻尔兹曼方程的尖锐全局适定性和散射 显示英文标题

标题： Sharp Global Well-posedness and Scattering of the Boltzmann Equation

摘要： 我们考虑具有角截断的麦克斯韦粒子和软势的三维玻尔兹曼方程。 我们证明了初始数据在尺度临界空间中较小时的尖锐全局适定性。 如果初始数据属于$L^{1}$，解仍然属于$L^{1}$，即使在如此低的正则性下也是如此。 存在性、唯一性和正则性准则的关键是新的双线性时空估计，用于增益项，其证明基于非线性色散PDE的新技术，包括原子$U$-$V$空间、多线性频率分析、色散估计等。 据我们所知，这是玻尔兹曼方程的第一个三维尖锐全局结果。 显示英文摘要

摘要： We consider the 3D Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff. We prove sharp global well-posedness with initial data small in the scaling-critical space. The solution also remains in $L^{1}$ if the initial datum is in $L^{1}$, even at such low regularity. The key to existence, uniqueness and regularity criteria is the new bilinear spacetime estimates for the gain term, the proof of which is based on novel techniques from nonlinear dispersive PDEs including the atomic $U$-$V$ spaces, multi-linear frequency analysis, dispersive estimates, etc. To our knowledge, this is the first 3D sharp global result for the Boltzmann equation.