Local well-posedness for the periodic higher order KdV type equations

被引：24

作者：

Hirayama, Hiroyuki ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2012年 / 19卷 / 06期

关键词：

KdV equation; Well-posedness; Cauchy problem; Fourier restriction norm; KORTEWEG-DEVRIES EQUATION; DE-VRIES EQUATION; CAUCHY-PROBLEM; KAWAHARA EQUATION; GLOBAL EXISTENCE; SOBOLEV SPACES;

D O I：

10.1007/s00030-011-0147-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Higher order KdV type equations are the equation replaced by a higher order derivative for the KdV equation. Recently, the local well-posedness result for these equations on torus have been given by Gorsky and Himonas (Math. Comput. Simul. 80:173-183, 2009). We extend this result by improving a bilinear estimate used in the Fourier restriction norm method.

引用

下载

页码：677 / 693

页数：17

共 50 条

[1] Local well-posedness for the periodic higher order KdV type equations
Hiroyuki Hirayama
Nonlinear Differential Equations and Applications NoDEA, 2012, 19 : 677 - 693
[2] Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations
Yi Hu
Xiaochun Li
The Journal of Geometric Analysis, 2015, 25 : 709 - 739
[3] Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations
Hu, Yi
Li, Xiaochun
JOURNAL OF GEOMETRIC ANALYSIS, 2015, 25 (02) : 709 - 739
[4] WELL-POSEDNESS OF KDV TYPE EQUATIONS
Carvajal, Xavier
Panthee, Mahendra
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[5] Local well-posedness for the fifth-order KdV equations on T
Kwak, Chulkwang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (10) : 7683 - 7737
[6] SHARP LOCAL WELL-POSEDNESS OF KDV TYPE EQUATIONS WITH DISSIPATIVE PERTURBATIONS
Carvajal, Xavier
Panthee, Mahendra
QUARTERLY OF APPLIED MATHEMATICS, 2016, 74 (03) : 571 - 594
[7] Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition
Kato, Takamori
Tsugawa, Kotaro
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 5 (03):
[8] LARGE DATA LOCAL WELL-POSEDNESS FOR A CLASS OF KDV-TYPE EQUATIONS
Harrop-Griffiths, Benjamin
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (02) : 755 - 773
[9] LOCAL WELL-POSEDNESS OF THE FIFTH-ORDER KDV-TYPE EQUATIONS ON THE HALF-LINE
Cavalcante, Marcio
Kwak, Chulkwang
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (05) : 2607 - 2661
[10] Local well-posedness for the dispersion generalized periodic KdV equation
Li, Junfeng
Shi, Shaoguang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 379 (02) : 706 - 718

← 1 2 3 4 5 →