Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	段仁军，香港中文大学
Inviter:
Title:	Quantitative properties of kinetic shear flow
Time & Venue:	2020.08.19 14:00-15:00 腾讯会议号：809 530 971
Abstract:	The uniform shear flow for a 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 additional heat and the system becomes far from an equilibrium state. In case of the Maxwell molecule model, we establish the unique existence, regularity, shear-rate-dependent structure and non-negativity of self-similar solutions for any small shear rate. The non-negativity is justified through the large time asymptotic stability in perturbation framework even in the spatially inhomogeneous setting, 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 work is joint with Shuangqian Liu. 会议链接：https://meeting.tencent.com/s/kR36sEKQJ1F4