学术报告

报告人：王勇（中科院应用数学所，助理研究员）

报告人简介：王勇现为中科院应用数学所助理研究员，于2012年7月在中科院数学与系统科学学院获得博士学位，师从国家杰出基金获得者黄飞敏研究员。王勇博士主要从事非线性偏微分方程的研究，特别是对可压缩流体与Boltzmann方程的整体适应性等问题有着深入系统的研究，取得了一系列重要的成果。迄今已在Arch. Rational Mech. Anal., SIAM J.Math. Anal., J. Differential Equations等期刊上发表论文十余篇。

题目：Global well-posedness of the Boltzmann equation with large amplitude initial data

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.

报告时间：2016年5月23日（星期一）上午10:30---11:30

报告地点：科技楼南楼702