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报告题目：Global well-posedness of the Boltzmann equation with large amplitude initial data
报 告 人：杨彤 教授（香港城市大学）
报告时间：2016年4月1日（周五）下午 4:00-5:00
报告地点：4号楼4318

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                                       数学学院
                                    2016年03月30日

报告摘要：
     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. This is a joint work with Renjun Duan, Feimin Huang and Yong Wang.