Long-time asymptotic behavior of the fifth-order modified KdV equation in low regularity spaces

被引：23
|
作者：
Liu, Nan [1 ]
Chen, Mingjuan [2 ]
Guo, Boling [3 ]
机构：
[1] Henan Univ, Sch Math & Stat, Kaifeng, Peoples R China
[2] Jinan Univ, Dept Math, Guangzhou 510632, Peoples R China
[3] Inst Appl Phys & Computat Math, Beijing, Peoples R China
来源：
STUDIES IN APPLIED MATHEMATICS | 2021年 / 147卷 / 01期
基金：
中国博士后科学基金;
关键词：
fifth‐ order modified Korteweg– de Vries equation; Fourier analysis; long‐ time asymptotics; low regularity; nonlinear steepest descent method; GLOBAL WELL-POSEDNESS; STEEPEST DESCENT METHOD; INVERSE SCATTERING; MODIFIED KORTEWEG; STABILITY; 1ST;
D O I：
10.1111/sapm.12379
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems and the Dbar approach, the long-time asymptotic behavior of solutions to the fifth-order modified KdV (Korteweg-de Vries) equation on the line is studied in the case of initial conditions that belong to some weighted Sobolev spaces. Using techniques in Fourier analysis and the idea of the I-method, we give its global well-posedness in lower regularity Sobolev spaces and then obtain the asymptotic behavior in these spaces with weights.
引用
收藏
页码：230 / 299
页数：70
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