报告人：王勇（中国科学院数学与系统科学研究院）

邀请人：雷远杰

报告时间：2021年11月16日（星期二）14:30-16:30

报告地点：腾讯会议 ID：551 863 531

报告题目：Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space

报告摘要：We establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space $x\in\mathbb{R}^3$ for general collision kernels.  Our approch is based on the Hilbert expansion, and  a recent $L^2-L^\infty$ framework.  In particular, we improve the $L^2$-estimate to be a localized version because the planar rarefaction wave is indeed a one-dimensional wave which makes the source terms to be not integrable in the $L^2$ energy estimate of  three dimensional problem. We also point out that the wave strength of rarefaction may be large.

报告人简介：王勇研究员2012年博士毕业于中科院数学与系统科学研究院，现任中科院数学与系统科学研究院副研究员。主要研究非线性双曲守恒律、可压缩Navier-Stokes方程、Boltzmann方程等方程的适定性和流体动力学极限。公开发表SCI论文20余篇，主要论文发表在 Advances in Mathematics、Archive Rational Mechanics Analysis 和 SIAM Journal in Mathematics Analysis 等国际著名刊物上。