The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity

被引:17
|
作者
Li, Yongsheng [1 ]
Huang, Jianhua [2 ]
Yan, Wei [3 ]
机构
[1] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[2] Natl Univ Def & Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China
[3] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
关键词
Ostrovsky equation; Cauchy problem; Critical regularity; Dyadic bilinear estimates; GLOBAL WELL-POSEDNESS; WEAK ROTATION LIMIT; INITIAL-VALUE PROBLEM; DE-VRIES EQUATION; SOLITARY WAVES; SCHRODINGER-EQUATION; POSITIVE DISPERSION; ILL-POSEDNESS; SPACES; STABILITY;
D O I
10.1016/j.jde.2015.03.007
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we investigate the Cauchy problem for the Ostrovsky equation partial derivative x (u(t) - beta partial derivative(3)(x)u + 1/2 partial derivative x(u(2))) - gamma u = 0, in the Sobolev space H-3/4(R). Here beta > 0(< 0) corresponds to the positive (negative) dispersion of the media, respectively. P. Isaza and J. Mejia (2006) [13], (2009) [15], K. Tsugawa (2009) [26] proved that the problem is locally well-posed in H-s (R) when s > -3/4 and ill-posed when s < -3/4. By using some modified Bourgain spaces, we prove that the problem is locally well-posed in H-3/4(R) with beta < 0 and gamma > 0. The new ingredient that we introduce in this paper is Lemmas 2.1-2.6. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码:1379 / 1408
页数:30
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