SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

doi:10.1016/S0252-9602(17)30058-9

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1061-1082.doi: 10.1016/S0252-9602(17)30058-9

SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

蒋敏杰¹, 闫威¹, 张贻民²

1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;
2. School of Science, Wuhan University of Technology, Wuhan 430070, China

收稿日期:2016-02-24 修回日期:2016-12-24 出版日期:2017-08-25 发布日期:2017-08-25
通讯作者: Wei YAN,E-mail:yanwei19821115@sina.cn E-mail:yanwei19821115@sina.cn
作者简介:Minjie JIANG,E-mail:1764915956@qq.com;Yimin ZHANG,E-mail:zhangym802@126.com
基金资助:
This work is supported by Natural Science Foundation of China NSFC (11401180 and 11471330). The second author is also supported by the Young Core Teachers Program of Henan Normal University (15A110033). The third author is also supported by the Fundamental Research Funds for the Central Universities (WUT:2017 IVA 075).

SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

Minjie JIANG¹, Wei YAN¹, Yimin ZHANG²

1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;
2. School of Science, Wuhan University of Technology, Wuhan 430070, China

Received:2016-02-24 Revised:2016-12-24 Online:2017-08-25 Published:2017-08-25
Contact: Wei YAN,E-mail:yanwei19821115@sina.cn E-mail:yanwei19821115@sina.cn
About author:Minjie JIANG,E-mail:1764915956@qq.com;Yimin ZHANG,E-mail:zhangym802@126.com
Supported by:
This work is supported by Natural Science Foundation of China NSFC (11401180 and 11471330). The second author is also supported by the Young Core Teachers Program of Henan Normal University (15A110033). The third author is also supported by the Fundamental Research Funds for the Central Universities (WUT:2017 IVA 075).

摘要/Abstract

摘要：

This current paper is devoted to the Cauchy problem for higher order dispersive equation
u_{t + ∂_x²ⁿ⁺¹u=∂_x(u∂_xⁿu) + ∂_x^n-1(u_x²), n ≥ 2, n ∈ N⁺.

By using Besov-type spaces, we prove that the associated problem is locally well-posed in H(-n/2 + 3/4,-1/2n)(R). The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H^(s,a)(R) with s < -n/2 + 3/4 and all a ∈ R.}

关键词: Cauchy problem, sharp well-posedness, modified Bourgain spaces

Abstract:

Key words: Cauchy problem, sharp well-posedness, modified Bourgain spaces

蒋敏杰, 闫威, 张贻民. SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION[J]. 数学物理学报(英文版), 2017, 37(4): 1061-1082.

Minjie JIANG, Wei YAN, Yimin ZHANG. SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION[J]. Acta mathematica scientia,Series B, 2017, 37(4): 1061-1082.

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SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION

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