学术报告
The uniform shear flow for the Boltzmann equation-刘双乾（暨南大学）
题目：The uniform shear flow for the Boltzmann equation
报告人：刘双乾教授（暨南大学）
时间：2020年12月2日（星期三）下午14:00-15:00
地点：线上腾讯会议（会议号：978 756 715）
Abstract : 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. This is a joint work with Prof. Renjun Duan.
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