报告题目：Global Well-posedness of the Boltzmann Equation with Large Amplitude Initial Data　　

　　报 告 人：王勇 中国科学院数学与系统科学研究院　　

　　时 间： 2017年1月14日（周六）10：00-12：00　　

　　地 点： 所综合楼三楼会议室　　

　　Abstract: The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$ approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\infty$ norm under some smallness condition on $L^1_xL^\infty_v$ norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in $L^\infty_{x,v}$ norm with explicit rates of convergence is also studied.