BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Renjun Duan (The Chinese University of Hong Kong) DTSTART:20201112T130000Z DTEND:20201112T135000Z DTSTAMP:20260423T035625Z UID:IMS/69 DESCRIPTION:Title: The Boltzmann equation for uniform shear flow\nby Renjun Duan (The Chines e University of Hong Kong) as part of PDE seminar via Zoom\n\n\nAbstract\n The uniform shear flow for the rarefied gas is governed by the time-depend ent spatially homogeneous Boltzmann equation with a linear shear force. Th e main feature of such flow is that the temperature may increase in time d ue to the shearing motion that induces viscous heat and the system becomes far from equilibrium. For Maxwell molecules\, we establish the unique exi stence\, regularity\, shear-rate-dependent structure and non-negativity of self-similar profiles for any small shear rate. The non-negativity is jus tified through the large time asymptotic stability even in spatially inhom ogeneous perturbation framework\, and the exponential rates of convergence are also obtained with the size proportional to the second order shear ra te. The analysis supports the numerical result that the self-similar profi le admits an algebraic high-velocity tail that is the key difficulty to ov ercome in the proof. This work is joint with Shuangqian Liu.\n LOCATION:https://researchseminars.org/talk/IMS/69/ END:VEVENT END:VCALENDAR