Sharp well-posedness for the Benjamin equation

被引：19

作者：

Chen, W. ^{[2
]}

Guo, Z. ^{[1
]}

Xiao, J. ^{[3
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 17期

关键词：

Benjamin equation; Bilinear estimate; Bourgain space; Local and global well-posedness; INITIAL-VALUE PROBLEM; DE-VRIES EQUATION; ONO-EQUATION; DISPERSIVE EQUATIONS; BILINEAR ESTIMATE; LOW-REGULARITY; SOLITARY-WAVE; ILL-POSEDNESS; KDV EQUATION; SPACE;

D O I：

10.1016/j.na.2011.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Having the ill-posedness in the range s < -3/4 of the Cauchy problem for the Benjamin equation with an initial H(s)(R) data, we prove that the already-established local well-posedness in the range s > -3/4 of this initial value problem is extendable to s = -3/4 and also that such a well-posed property is globally valid for s is an element of [-3/4, infinity). (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：6209 / 6230

页数：22

共 29 条

[1]

Albert JP, 1999, SIAM J APPL MATH, V59, P2139

[2]

Angulo J., 1999, J DIFFER EQUATIONS, V152, P136, DOI DOI 10.1006/jdeq.1998.3525

[3] Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrodinger equation [J].

Bejenaru, I ;

Tao, T .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 233 (01) :228-259

[4] A NEW KIND OF SOLITARY WAVE [J].

BENJAMIN, TB .

JOURNAL OF FLUID MECHANICS, 1992, 245 :401-411

[5]

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

[6]

Bourgain J., 1997, Selecta Math. (N.S.), V3, P115

[7]

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

[8] On well-posedness for the Benjamin-Ono equation [J].

Burq, Nicolas ;

Planchon, Fabrice .

MATHEMATISCHE ANNALEN, 2008, 340 (03) :497-542

[9]

Chen Hongqiu, 1998, Adv. Differential Equations, V3, P51

[10] A Sharp Bilinear Estimate for the Bourgain-Type Space with Application to the Benjamin Equation [J].

Chen, Wengu ;

Xiao, Jie .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (10) :1739-1762

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