Cauchy problem of nonlinear dispersive equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400158
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Nagoya University
• Principal Investigator: Tsugawa Kotaro 名古屋大学, 多元数理科学研究科, 准教授 (70402451)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 分散型方程式 / 適切性 / 初期値問題 / 調和解析 / シュレディンガー方程式 / KdV方程式

Outline of Final Research Achievements

First, we proved the global well-posedness and asymptotic behavior of the Cauchy problem of Zakharov system in higher dimensions. We used the theory of Up, Vp space to prove it. The main difficulty comes from the difference of the properties of the linear equations. To overcome it, we used the intersection space of V2 space and Lebesgue space related to the end-point Strichartz estimate. Second, we categolized the fifth order KdV type equations. By using the normal form reduction, energy method and Bona-Smith approximation, we proved that the local well-posedness and parabolic smoothing effect.

Free Research Field

偏微分方程式論