Low regularity for the fifth order Kadomtsev-Petviashvili-I type equation

被引：4

作者：

Guo, Boling ^{[1
]}

Huo, Zhaohui ^{[2
]}

Fang, Shaomei ^{[3
]}

机构：

[1] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China

[2] Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

[3] South China Agr Univ, Dept Appl Math, Guangzhou 510642, Guangdong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 09期

关键词：

Well-posedness; Fifth order Kadomtsev-Petviashvili-I equation; Dyadic X-s; X-b spaces; GLOBAL WELL-POSEDNESS; CAUCHY-PROBLEM; SOBOLEV SPACES;

D O I：

10.1016/j.jde.2017.06.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Cauchy problem of the fifth order Kadomtsev-Petviashvili-I equation (fifth-KP-1) partial derivative(t)u + partial derivative(5)(x)u +/- partial derivative(3)(x)u - partial derivative(-1)(x)partial derivative(yy)u+partial derivative(x)(u(2)) = 0, (x, y, t) epsilon R-3; is considered. It follows that the fifth order Kadomtsev-Petviashvili-I equation (0.1) is locally well -posed in H-s,H-O with s >= -3/4, where the norm H-s,H-r is defined by ||f || H-(x.y)(s,r) = || <xi >(s) <zeta >(r) (f) over cap|| L-(xi,zeta)(2) . (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：5696 / 5726

页数：31

共 27 条

[1]

Bourgain J., 1993, Geom. Funct. Anal., V3, P107

[2]

Bourgain J., 1993, GEOM FUNCT ANAL, V3, P315

[3]

Bourgain J., 1993, The KdV equations, GAGA, V3, P209, DOI 10.1007/BF01895688

[4] Solitary waves of generalized Kadomtsev-Petviashvili equations [J].

deBouard, A ;

Saut, JC .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :211-236

[5] Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves [J].

DeBouard, A ;

Saut, JC .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (05) :1064-1085

[6] On the local regularity of the KP-I equation in anisotropic Sobolev space [J].

Guo, Zihua ;

Peng, Lizhong ;

Wang, Baoxiang .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2010, 94 (04) :414-432

[7] Global well-posedness of the KP-I initial-value problem in the energy space [J].

Ionescu, A. D. ;

Kenig, C. E. ;

Tataru, D. .

INVENTIONES MATHEMATICAE, 2008, 173 (02) :265-304

[8] Global well-posedness of the Benjamin-Ono equation in low-regularity spaces [J].

Ionescu, Alexandru D. ;

Kenig, Carlos E. .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (03) :753-798

[9]

Kadomtsev B. B., 1970, Soviet Physics - Doklady, V15, P539

[10] DYNAMICS OF 2-DIMENSIONAL SOLITONS IN WEAKLY DISPERSIVE MEDIA [J].

KARPMAN, VI ;

BELASHOV, VY .

PHYSICS LETTERS A, 1991, 154 (3-4) :131-139

← 1 2 3 →