Institute of Mathematics for Industry

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[2018.8.20]Analysis Seminar


Hold Date 2018-08-20 13:20~2018-08-20 17:30

Place Seminar Room W1-D-625, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Yachun Li (Shanghai Jiao Tong University), Myoungjean Bae (Pohang University of Science and Technology), Chunjing Xie (Shanghai Jiao Tong University), Jan Brezina (Tokyo Institute of Technology)

Program:
13:20 - 14:10
Yachun Li (Shanghai Jiao Tong University)
Qualitative Studies on Radiation Hydrodynamics Equations
14:25 - 15:15
Myoungjean Bae (Pohang University of Science and Technology)
Global existence of weak shocks past solid ramps
15:30 - 16:20
Chunjing Xie (Shanghai Jiao Tong University)
Some studies on steady flows in channels
16:40 - 17:30
Jan Brezina (Tokyo Institute of Technology)
Measure-valued solutions and Navier-Stokes-Fourier system


Abstract 1 (Yachun Li (Shanghai Jiao Tong University)):
In this talk I will present recent progress on viscous or inviscid radiation hydrodynamics equations for compressible fluids. The results include the local existence of classical solutions with vacuum, some blow-up results of classical solutions, and some regularity criteria.

Abstract 2 (Myoungjean Bae (Pohang University of Science and Technology)):
When a steady supersonic flow impinges onto a solid wedge whose angle is less than a critical angle, so called detachment angle, there are two possible configurations: the weak shock solution and the strong shock solution. It is widely conjectured that the weak shock solution is physically admissible since it is the one observed experimentally. This is called ‘Prandtl’s conjecture’. In this talk, I address this longstanding open conjecture, and present recent analysis to establish the stability theorem for steady weak shock solutions as the long-time asymptotics of unsteady flows for all the physical parameters up to the detachment angle for potential flow. This talk is based on joint work with Gui-Qiang G. Chen (Univ. of Oxford) and Mikhail Feldman (UW-Madison).

Abstract 3 (Chunjing Xie (Shanghai Jiao Tong University)):
In this talk, both the inviscid and viscous flows in channels will be investigated. We will first address the well-posedness for steady inviscid compressible flows in nozzles with emphasis on the fine properties of subsonic flows in nozzles. Then we study the stability of some special viscous flows in channels with the aid of some weighted energy estimate.

Abstract 4 (Jan Brezina (Tokyo Institute of Technology)):
Encouraged by the ideas and results obtained when studying measure-valued solutions for the Complete Euler system we introduce measure-valued solutions to the Navier-Stokes-Fourier system and show weak-strong uniqueness. Namely, we identify a large class of objects that we call dissipative measure-valued (DMV) solutions, in which the strong solutions are stable. That is, a (DMV) solution coincides with the strong solution emanating from the same initial data as long as the latter exists.

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