On the lifespan and asymptotic behavior of solutions to systems of wave equations with nonlinear terms of long range effects

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04955
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Mie University
• Principal Investigator: HIDANO KUNIO 三重大学, 教育学部, 教授 (00285090)
• Co-Investigator(Kenkyū-buntansha): 横山 和義 北海道科学大学, 工学部, 准教授 (20316243)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: nonlinear wave equations / weak null condition

Outline of Final Research Achievements

In 2003, Lindblad and Rodnianski conjectured that the Cauchy problem for nonlinear wave equations satisfying the weak null condition would admit global (in time) solutions for small and smooth data. Using the ghost weight method due to Alinhac, we have studied the Cauchy problem for a system of quasi-linear wave equations satisfying this condition and proved that it admits global solutions for small and smooth data. Our result will be one of the basic steps toward the resolution of their conjecture.

Free Research Field

数物系科学