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

被引：24

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

页码：230 / 299

页数：70

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