Sharp Constant of an Anisotropic Gagliardo-Nirenberg-Type Inequality and Applications

被引：13

作者：

Esfahani, Amin ^{[1
,2
]}

Pastor, Ademir ^{[3
]}

机构：

[1] Damghan Univ, Sch Math & Comp Sci, Damghan 36715364, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran 193955746, Iran

[3] IMECC UNICAMP, Rua Sergio Buarque Holanda,651,Cidade Univ, BR-13083859 Campinas, SP, Brazil

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2017年 / 48卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Fractional Sobolev-Liouville inequality; BO-ZK equation; Gagliardo-Nirenberg inequality; ZAKHAROV-KUZNETSOV EQUATION; SCATTERING; STABILITY; DECAY;

D O I：

10.1007/s00574-016-0017-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish the best constant of an anisotropic GagliardoNirenberg-type inequality related to the Benjamin-Ono-Zakharov-Kuznetsov equation. As an application of our results, we prove the uniform bound of solutions for such a equation in the energy space.

引用

页码：171 / 185

页数：15

共 32 条

[1] Scaling, stability and singularities for nonlinear, dispersive wave equations: the critical case [J].

Angulo, J ;

Bona, JL ;

Linares, F ;

Scialom, M .

NONLINEARITY, 2002, 15 (03) :759-786

[2]

[Anonymous], 1963, Mat. Sb

[3]

[Anonymous], 1941, Acta Sci. Math.

[4]

Begout P., 2002, Adv. Math. Sci. Appl, V12, P817

[5] Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems [J].

Bellazzini, Jacopo ;

Frank, Rupert L. ;

Visciglia, Nicola .

MATHEMATISCHE ANNALEN, 2014, 360 (3-4) :653-673

[6] INTERNAL WAVES OF PERMANENT FORM IN FLUIDS OF GREAT DEPTH [J].

BENJAMIN, TB .

JOURNAL OF FLUID MECHANICS, 1967, 29 :559-&

[7] Decay and analyticity of solitary waves [J].

Bona, JL ;

Li, YA .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (05) :377-430

[8]

Bourgain J., 2002, J ANAL MATH, V87, P439

[9] Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces [J].

Brezis, Haim ;

Mironescu, Petru .

JOURNAL OF EVOLUTION EQUATIONS, 2001, 1 (04) :387-404

[10] On the uniform bound of solutions for the KP-type equations [J].

Chen, Jianqing ;

Feng, Baofeng ;

Liu, Yue .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) :E2062-E2069

← 1 2 3 4 →