Well-posedness of the Cauchy problem for Ostrovsky, Stepanyams and Tsimring equation with low regularity data

被引：8

作者：

Zhao, Xiangqing ^{[1
]}

Cui, Shangbin ^{[2
]}

机构：

[1] Zhejiang Ocean Univ, Dept Math, Zhoushan 316000, Zhejiang, Peoples R China

[2] Sun Yat Sen Univ, Inst Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 344卷 / 02期

基金：

中国国家自然科学基金;

关键词：

OST equation; initial value problem; local well-posedness; global well-posedness;

D O I：

10.1016/j.jmaa.2008.03.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

this paper we prove that the initial value problem of the OST equation u(t) + u(xxx) + eta(Hu(x) + Hu(xxx)) + uu(x) = 0 (x is an element of R, t >= 0), where eta > 0 and H denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space H-s(R) when s > -3/4, and globally well-posed in H-s(R) when s >= 0. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：778 / 787

页数：10

共 50 条

[41] Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux
G. M. Coclite
N. Chatterjee
N. H. Risebro
Milan Journal of Mathematics, 2019, 87 : 283 - 301
[42] WELL-POSEDNESS, REGULARITY AND EXACT CONTROLLABILITY FOR THE PROBLEM OF TRANSMISSION OF THE SCHRODINGER EQUATION
Allag, I.
Rebiai, S. E.
QUARTERLY OF APPLIED MATHEMATICS, 2014, 72 (01) : 93 - 108
[43] THE WELL-POSEDNESS AND REGULARITY OF A ROTATING BLADES EQUATION
Shen, Lin
Wang, Shu
Wang, Yongxin
ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 691 - 719
[44] The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
Li, Yongsheng
Huang, Jianhua
Yan, Wei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (04) : 1379 - 1408
[45] Remarks on the well-posedness of the nonlinear Cauchy problem
Métivier, G
GEOMETRIC ANALYSIS OF PDE AND SEVERAL COMPLEX VARIABLES: DEDICATED TO FRANCOIS TREVES, 2005, 368 : 337 - 356
[46] On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions
Prokhorov, I. V.
Sushchenko, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (04) : 736 - 745
[47] The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise
I. V. Melnikova
M. A. Alshanskiy
Proceedings of the Steklov Institute of Mathematics, 2013, 280 : 134 - 150
[48] Well-posedness of the Cauchy problem for the fourth-order nonlinear Schrodinger equation
Chen, Mingjuan
Liu, Nan
Wang, Yaqing
APPLIED MATHEMATICS LETTERS, 2025, 160
[49] The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise
Melnikova, I. V.
Alshanskiy, M. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 280 : 134 - 150
[50] SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION
蒋敏杰
闫威
张贻民
Acta Mathematica Scientia, 2017, (04) : 1061 - 1082

← 1 2 3 4 5 →