マス・フォア・インダストリ研究所

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解析セミナー(2018.8.20)


開催時期 2018-08-20 13:20~2018-08-20 17:30

場所 九州大学 伊都キャンパス ウエスト1号館 中セミナー室 W1-D-625

受講対象  

講師 Yachun Li (上海交通大学), Myoungjean Bae (浦項工科大学校), Chunjing Xie (上海交通大学), Jan Brezina (東京工業大学)

プログラム:
13:20 - 14:10
Yachun Li (上海交通大学)
Qualitative Studies on Radiation Hydrodynamics Equations
14:25 - 15:15
Myoungjean Bae (浦項工科大学校)
Global existence of weak shocks past solid ramps
15:30 - 16:20
Chunjing Xie (上海交通大学)
Some studies on steady flows in channels
16:40 - 17:30
Jan Brezina (東京工業大学)
Measure-valued solutions and Navier-Stokes-Fourier system


要旨 1 (Yachun Li (上海交通大学))
    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.

要旨 2 (Myoungjean Bae (浦項工科大学校))
    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).

要旨 3 (Chunjing Xie (上海交通大学))
    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.

要旨 4 (Jan Brezina (東京工業大学))
    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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