报告人: : Feimin Huang黄飞敏(Chinese Academy of Sciences) 

报告题目: Macroscopic regularity for the Boltzmann equation

报告人简介：黄飞敏，男，1971年12月出生，中国科学院数学与系统科学研究院研究员，杰青获得者。2011年被聘为华罗庚应用数学首席研究员。1999-2000年在意大利国际高等研究院(SISSA)做博士后，2001-2003年在日本大阪大学做日本学术振兴会(JSPS)外国人特别研究员，此外短期访问的国外著名学府有美国斯坦福大学，布朗大学等。黄飞敏在双曲守恒律方程组做出了重要贡献，证明了等温气体动力学方程组弱解的整体存在性。获得的奖励有美国工业及应用数学学会杰出论文奖(The SIAM Outstanding Paper Prize)，国家自然科学二等奖。

报告摘要: The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated.It is shown that the macroscopic parts of solutions to the Boltzmann equation, i.e. the density, momentum and total energy are continuous functions of $(x,t)$ in the region $\mathbb{R}^3\times(0,+\infty)$. More precisely, these macroscopic quantities immediately become continuous in any positive time even though they are initially discontinuous and the discontinuities of solutions propagate only in the microscopic level.It should be noted that such kind of phenomenon  can not happen for the compressible Navier-Stokes equations in which the initial discontinuities of the density never vanish in any finite time.This hints that the Boltzmann equation has better regularityeffect in the macroscopic level than compressible Navier-Stokes equations.

报告时间： 2016年11月11日（星期五）上午11：00-12：00.

报告地点：科技南楼702