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

被引：25
|
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
收藏
页码：677 / 693
页数：17
相关论文
共 50 条
  • [41] GLOBAL WELL-POSEDNESS FOR A SYSTEM OF KDV-TYPE EQUATIONS WITH COUPLED QUADRATIC NONLINEARITIES
    Bona, Jerry L.
    Cohen, Jonathan
    Wang, Gang
    NAGOYA MATHEMATICAL JOURNAL, 2014, 215 : 67 - 149
  • [42] Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type Equations
    Xavier Carvajal
    Amin Esfahani
    Mahendra Panthee
    Bulletin of the Brazilian Mathematical Society, New Series, 2017, 48 : 505 - 550
  • [43] Well-Posedness Results and Dissipative Limit of High Dimensional KdV-Type Equations
    Carvajal, Xavier
    Esfahani, Amin
    Panthee, Mahendra
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2017, 48 (04): : 505 - 550
  • [44] An improved local well-posedness result for the modified KdV equation
    Grünrock, A
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (61) : 3287 - 3308
  • [45] Well-posedness for parabolic equations of arbitrary order
    Marchi, C
    ASYMPTOTIC ANALYSIS, 2003, 35 (01) : 41 - 64
  • [46] Local well-posedness for the homogeneous Euler equations
    Zhong, Xin
    Wu, Xing-Ping
    Tang, Chun-Lei
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) : 3829 - 3848
  • [47] LOCAL WELL-POSEDNESS OF NONLOCAL BURGERS EQUATIONS
    Benzoni-Gavage, Sylvie
    DIFFERENTIAL AND INTEGRAL EQUATIONS, 2009, 22 (3-4) : 303 - 320
  • [48] ON THE SOLVABILITY AND WELL-POSEDNESS OF INITIAL PROBLEMS FOR NONLINEAR HYPERBOLIC EQUATIONS OF HIGHER ORDER
    Grigolia, M.
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2005, 35 : 37 - 54
  • [49] GLOBAL WELL-POSEDNESS OF NLS-KDV SYSTEMS FOR PERIODIC FUNCTIONS
    Matheus, Carlos
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
  • [50] Local Well-posedness for Semilinear Heat Equations on H type Groups
    Oka, Yasuyuki
    TAIWANESE JOURNAL OF MATHEMATICS, 2018, 22 (05): : 1091 - 1105
12345