Concentration Phenomena and Structure of Solution for Nonlinear Evolution Equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 23224003
• Research Category: Grant-in-Aid for Scientific Research (S)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: Tsutsumi Yoshio 京都大学, 理学(系)研究科(研究院), 教授 (10180027)
• Co-Investigator(Kenkyū-buntansha): Okamoto Hisashi 京都大学, 数理解析研究所, 教授 (40143359) ; Nakanishi Kenji 大阪大学, 大学院情報科学研究科, 教授 (40322200) ; Sawano Yoshihiro 首都大学東京, 大学院理工学研究科, 准教授 (40532635) ; Kishimoto Nobu 京都大学, 数理解析研究所, 講師 (90610072)
• Co-Investigator(Renkei-kenkyūsha): Takaoka Hideo 北海道大学, 大学院理学研究院, 教授 (10322794) ; Mizoguchi Noriko 東京学芸大学, 教育学部, 准教授 (00251570) ; Maeda Masaya 千葉大学, 大学院理学研究科, 准教授 (40615001) ; Kato Takamori 佐賀大学, 大学院工学系研究科, 講師 (50620639) ; Miyaji Tomoyuki 明治大学, 研究・知財戦略機構, 特任講師 (20613342) ; Sasaki Youhei 京都大学, 大学院理学研究科, 助教 (70583459)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 非線形波動・分散型方程式 / 非圧縮性Navier-Stokes方程式 / 解の特異性と凝縮現象 / Keller-Segel方程式 / 解の時間大域挙動 / Gibbs測度 / Stokesドリフト

Outline of Final Research Achievements

For nonlinear wave and dispersive equations, in collaboration with Schlag, Nakanishi succeeded in classifying the global behavior of any solutions starting near an unstable ground state. This is a breakthrough, because there were no results available beofre their papers. Tsutsumi, together with Yoshikawa, proved the existence of two invariant measures for the isothermal Falk model. One is the Gibbs measure and another is an invariant measure proposed by Kuksin. In collaboration with Shoji, Okamoto investigated the Stokes drift of surface gravity waves with surface tension. Okamoto and Shoji proved that the orbits of particles are not closed curves by the method of the complex analysis.

Free Research Field

函数方程式論