Existence and global behavior of spatially periodic solutions to the initial value problems for nonlinear dispersive equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740086
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: Kishimoto Nobu 京都大学, 数理解析研究所, 講師 (90610072)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 非線形分散型方程式 / 初期値問題 / 適切性 / 周期境界条件 / 無条件一意性

Outline of Final Research Achievements

We investigated the spatially periodic solutions of nonlinear dispersive partial differential equations arising as important models in various fields of physics and engineering. In particular, we studied unconditional uniqueness for the initial value problem, namely, uniqueness of solutions in a natural class. We succeeded in providing a general framework applicable to a wide range of nonlinear dispersive equations, and applied it to some specific problems for which unconditional uniqueness had been open. Moreover, for the nonlinear Schroedinger equation and an equation for rotating fluids, we analyzed the interactions between resonant frequencies, which seem important in controlling the nonlinear interactions, by use of some techniques from combinatorics and elementary number theory.

Free Research Field

非線形偏微分方程式