时间：2016年6月23日（周四）15：00——16:00

地点：下沙校区教学D204学术报告厅

摘要：

The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this talk, the case with angular cut-off is presented. 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 regularity effect in the macroscopic level than compressible Navier-Stokes equations.

专家简介：

黄飞敏，男，中国科学院数学与系统科学研究院华罗庚首席研究员，国家杰出青年基金获得者，北京市数学会理事，研究领域为非线性偏微分方程。2004年因解决一个数学难题获美国工业及应用数学学会杰出论文奖(The SIAM Outstanding Paper Prize)。2011年获中国科学院青年科学家奖，2013年获国家自然科学二等奖（第一完成人），2013年入选中青年科技创新领军人才计划。是《应用数学学报》编委、《数学物理学报》编委、《Kinectic & Related Models》编委。