京都大学 NLPDE セミナー

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 15:30 〜 17:30
会場
京都大学 理学研究科 3 号館 251 号室 (会場へのアクセス
Room 251 at Science Building No.3, Kyoto University (map
幹事
堤誉志雄, 前川泰則, 岸本展, 阿部健, 池田正弘, 山崎陽平


次回のセミナーの予定
Upcoming seminar

● 2016 年 9 月 2 日 16:00 〜 17:30
講演者
呉 忠弘 氏 (The University of Edinburgh)
Tadahiro Oh (The University of Edinburgh)
講演題目
On the deterministic and probabilistic well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces
講演要旨
We consider the Cauchy problem for the cubic fourth order NLS (4NLS) on the circle in low regularities. First, we show that the 4NLS is strongly ill-posed below L^2. Then, we consider well-posedness of the renormalized 4NLS in both deterministic and probabilistic setting. In the deterministic setting, we prove global well-posedness in some negative Sobolev spaces by the short time Fourier restriction norm method. In particular, uniqueness is obtained by establishing an estimate on the difference to two solutions via an infinite iteration of normal form reductions. In the probabilistic setting, we prove that white noise is invariant under the dynamics of the renormalized 4NLS by introducing a random resonant-nonlinear decomposition and establishing a probabilistic a priori bound.


今後のセミナーの予定
Schedules of future seminars

9 月 2 日
呉 忠弘 氏 (The University of Edinburgh)
Tadahiro Oh (The University of Edinburgh)