标题：Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space

报告人：王勇（中科院数学与系统科学研究院）

地点：数学与计算机科学学院4号楼302室

时间：2019年11月5日上午9：00

摘要：In this paper, 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 a generalized 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.

报告人介绍：王勇2012年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渐近行为。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 等刊物上。主持国家自然科学基金一项，中科院基金一项。