主讲人简介：黄飞敏，中科院数学与系统科学研究院应用数学研究所所长助理，研究员、博士生导师。2003年获首届中国科学院数学与系统科学研究院“突出科研成果奖”，2004年获美国工业及应用数学协会“杰出论文奖”(The SIAM Outstanding Paper Prize)，2007年获得中国科学院数学与系统科学研究院优秀教师奖，2008年获国家杰出青年科学基金。

内容摘要：The regularity of solutions to the Boltzmannequation is a fundamental problem in the kinetic theory. In this paper, thecase with angular cut-off is investigated.  It is shown thatthe macroscopic parts  of  solutions to the Boltzmannequation, i.e. the density, momentum and total energy  are continuousfunctions  of $(x,t)$ in the region $\mathbb{R}^3\times(0,+\infty)$. Moreprecisely,  these macroscopic quantities immediately becomecontinuous in any positive time even though they are initially discontinuousand the discontinuities of solutions propagate only in the microscopic level.It should be noted that such kind of phenomenon  can not happen for thecompressible Navier-Stokes equations in which the initial discontinuities ofthe density never vanish in any finite time. This hints that the Boltzmannequation has better regularityeffect in the macroscopic levelthan compressible Navier-Stokes equations.

讲座主持：秦玉明

讲座语言：英文