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解析学火曜セミナー
過去の記録 ～10/18｜次回の予定｜今後の予定 10/19～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 号室 |
|---|---|
| 担当者 | 石毛 和弘，宮本 安人，坂井 秀隆，三竹 大寿，高田 了 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
次回の予定
2025年10月28日(火)
15:00-17:30 数理科学研究科棟(駒場) 002号室
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
[ 講演概要 ]
Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
木下 真也 氏 (名古屋大学) 16:30-17:30Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
[ 講演概要 ]
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
