Asymptotic analysis for systems of dispersive equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654034
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: HAYASHI Nakao 大阪大学, 理学(系)研究科(研究院), 教授 (30173016)
• Co-Investigator(Renkei-kenkyūsha): SUNAGAWA Hideaki 大阪大学, 大学院理学研究科, 准教授 (80375394)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 分散型波動方程式系 / 漸近的振舞い / 臨界べき非線形項 / 修正波動作用素 / Schroedinger方程式系 / Klein-Gordon方程式系

Outline of Final Research Achievements

We considered systems of nonlinear dispersive equations including nonlinear Schoedinger systems and nonlinear Klein-Gordon systems with quadratic interactions in two space dimensions. We showed the existence of modified wave operators for nonlinear Schroedinger systems under the mass resonance condition and non existence of wave operator by using a sharp time decay estimate of solutions to linear problem from below. For nonlinear Klein-Gordon systems, the initial value problem was considered when the initial data are in the class which is close to the energy one and the existence of scattering states was established under some mass non resonance conditions.

Free Research Field

偏微分方程式