勷勤数学•专家报告

题      目：3D hard sphere Boltzmann equation: explicit structure and the transition process from polynomial tail to Gaussian tail

报  告  人：王海涛  教授  (邀请人：喻洪俊)

                                  上海交通大学

时      间：10月18日  15：00-16：00

地     点：学院西楼二楼会议室

报告人简介:

       王海涛，2010年本科毕业于上海交通大学，2015年博士毕业于新加坡国立大学，2015-2017在“中央研究院”从事博士后研究，2017年7月加入上海交通大学。他主要的研究兴趣是对动理学、流体力学初边值问题的解给出精细刻画，所得结果发表在 Arch. Ration. Mech. Anal., SIAM J. Math. Anal., J. Stat. Phys.等期刊上，曾应邀作世界华人数学家大会45分钟邀请报告。

摘      要：

       We study the Boltzmann equation with hard sphere in a near-equilibrium setting. The initial data is compactly supported in the space variable and has a polynomial tail in the microscopic velocity. We show that the solution can be decomposed into a particle-like part (polynomial tail) and a fluid-like part (Gaussian tail). The particle-like part decays exponentially in both space and time, while the fluid-like part dominates the long time behavior and exhibits rich wave motion. The nonlinear wave interactions in the fluid-like part are precisely characterized. Furthermore, the transition process from the polynomial to the Gaussian tail is quantitatively revealed.

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