报告人：刘双乾（华中师范大学）

邀请人：雷远杰

报告题目：The Boltzmann equation for uniform shear flow

报告摘要：The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in time due to the shearing motion that induces viscous heat and the system becomes far from equilibrium. For Maxwell molecules, we establish the unique existence, regularity, shear-rate-dependent structure and non-negativity of self-similar profiles for any small shear rate. The non-negativity is justified through the large time asymptotic stability even in spatially inhomogeneous perturbation framework, and the exponential rates of convergence are also obtained with the size proportional to the second order shear rate. The analysis supports the numerical result that the self-similar profile admits an algebraic high-velocity tail that is the key difficulty to overcome in the proof.

报告人简介：刘双乾：教授，华中师范大学sunbet中国官网，2009年博士毕业于武汉大学，主要研究方向为动理学方程及相关模型的数学理论。近五年先后在CPAM,ARMA,CMP,JFA等国际主流数学杂志发表论文数十篇。

报告时间: 2020年10月2日（星期五）下午15:30-17:30

报告地点：科技南楼702