Scattering for the quartic generalised Korteweg-de Vries equation

被引：55

作者：

Tao, Terence ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 232卷 / 02期

关键词：

KdV; gKdV; scattering; soliton; asymptotic stability; critical regularity;

D O I：

10.1016/j.jde.2006.07.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the quartic generalised KdV equation U-t + U-xxx + (U-4)(x) = 0 is globally well posed for data in the critical (scale-invariant) space, (R) with small norm (and locally well posed for large norm), improving a result of Grumrock [A. Grunrock, A bilinear Airy-estimate with application to gKdV-3, Differential Integral Equations 18 (12) (2005) 1333-1339]. As an application we obtain scattering results in H-x(1)(R) boolean AND H-x(-1/6) (R) for the radiation component of a perturbed soliton for this equation, improving the asymptotic stability results of Martel and Merle [Y. Martel, F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157 (3) (2001) 219-254]. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：623 / 651

页数：29

共 14 条

[1]

BEJENARU I, MATHAP0604255

[2]

Christ M, 2003, AM J MATH, V125, P1235

[3] Sharp global well-posedness for KDV and modified KDV on R and T [J].

Colliander, J ;

Keel, M ;

Staffilani, G ;

Takaoka, H ;

Tao, T .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 16 (03) :705-749

[4]

COTE R, 2006, ECOLE NORMALE SUPERI

[5]

Côte R, 2006, DIFFER INTEGRAL EQU, V19, P163

[6]

Grünrock A, 2005, DIFFER INTEGRAL EQU, V18, P1333

[7]

IONESCU A, MATHAP0605209

[8] WELL-POSEDNESS AND SCATTERING RESULTS FOR THE GENERALIZED KORTEWEG-DEVRIES EQUATION VIA THE CONTRACTION PRINCIPLE [J].

KENIG, CE ;

PONCE, G ;

VEGA, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (04) :527-620

[9] Asymptotic stability of solitons of the subcritical gKdV equations revisited [J].

Martel, Y ;

Merle, F .

NONLINEARITY, 2005, 18 (01) :55-80

[10] Asymptotic stability of solitons for subcritical generalized KdV equations [J].

Martel, Y ;

Merle, F .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 157 (03) :219-254

← 1 2 →