京都大学 NLPDE セミナー
Kyoto University NLPDE Seminar
このセミナーは非線形微分方程式を中心に解析の研究に関して討論するセミナーです．
- 日時
- 毎週金曜日 Every Friday 16:00 〜 17:00
- 開催方法
-
ハイブリッド または 完全オンライン
zoom での聴講をご希望の方はセミナーの 2 日前までに，いずれかの幹事へメールでご連絡ください． 但し，人数の都合上ご希望に添えない場合があります． - 幹事
- 清水扇丈， 中西賢次， 前川泰則， 高棹圭介， 筒井容平， 林雅行， 三浦達哉， 岸本展， 清水一慶， 青木基記， 大山広樹
次回のセミナーの予定
Upcoming seminar
- 講演者
- Slim Ibrahim 氏 （University of Victoria）
- 講演題目
- Stable singularity formation for the inviscid Primitive equations
- 講演要旨
- The primitive equations (PEs) model large-scale dynamics of the oceans and the atmosphere. While it is by now well known that the three-dimensional viscous PEs are globally well posed in Sobolev spaces, and that there are solutions to the inviscid PEs (also called the hydrostatic Euler equations) that develop singularities in finite time, the qualitative description of the blowup still remains undiscovered. In this talk, we provide a full description of two blow-up mechanisms, for a reduced PDE that is satisfied by a class of particular solutions to the PEs. In the first one a shock forms, and pressure effects are subleading, but in a critical way: they localize the singularity closer and closer to the boundary near the blow-up time (with a logarithmic-in-time law). This first mechanism involves a smooth blow-up profile and is stable among smooth enough solutions. In the second one the pressure effects are fully negligible; this dynamics involves a two-parameter family of non-smooth profiles, and is stable only by smoother perturbations. At the end, I will briefly discuss how the results extend when the system is coupled with a density equation. These are joint works with C. Collot, Q. Lin, Titi and Qian.
今後のセミナーの予定
Schedules of future seminars
- 7 月 4 日
- Slim Ibrahim 氏 （University of Victoria）
- 7 月 11 日
- Sanghyuk Lee 氏 （Seoul National University）
- 7 月 18 日
- 柳田 英二 氏 （東京大学）
Eiji Yanagida (The University of Tokyo) - 7 月 25 日
- 岡本 葵 氏 （広島大学）
Mamoru Okamoto (Hiroshima University)