LARGE DATA LOCAL WELL-POSEDNESS FOR A CLASS OF KDV-TYPE EQUATIONS

被引：0
|
作者：
Harrop-Griffiths, Benjamin [1 ]
机构：
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 02期
关键词：
NONLINEAR DISPERSIVE EQUATIONS; SCHRODINGER-EQUATIONS; CAUCHY-PROBLEM;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we consider the Cauchy problem with large initial data for an equation of the form (partial derivative(t) + partial derivative(3)(x)) u = F(u, u(x), u(xx)) where F is a polynomial with no constant or linear terms. Local well-posedness was established in weighted Sobolev spaces by Kenig-Ponce-Vega. In this paper we prove local well-posedness in a translation invariant subspace of Hs by adapting the result of Marzuola-Metcalfe-Tataru on quasilinear Schrodinger equations.
引用
收藏
页码：755 / 773
页数：19
相关论文
共 50 条
  • [1] Large Data Local Well-Posedness for a Class of KdV-Type Equations II
    Harrop-Griffiths, Benjamin
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (18) : 8590 - 8619
  • [2] Well-posedness for KdV-type equations with quadratic nonlinearity
    Hirayama, Hiroyuki
    Kinoshita, Shinya
    Okamoto, Mamoru
    JOURNAL OF EVOLUTION EQUATIONS, 2020, 20 (03) : 811 - 835
  • [3] Local well-posedness of a nonlinear KdV-type equation
    Israwi, Samer
    Talhouk, Raafat
    COMPTES RENDUS MATHEMATIQUE, 2013, 351 (23-24) : 895 - 899
  • [4] Well-posedness for KdV-type equations with quadratic nonlinearity
    Hiroyuki Hirayama
    Shinya Kinoshita
    Mamoru Okamoto
    Journal of Evolution Equations, 2020, 20 : 811 - 835
  • [5] Local well-posedness for a fractional KdV-type equation
    Roger P. de Moura
    Ailton C. Nascimento
    Gleison N. Santos
    Journal of Evolution Equations, 2022, 22
  • [6] Local well-posedness for a fractional KdV-type equation
    De Moura, Roger P.
    Nascimento, Ailton C.
    Santos, Gleison N.
    JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (01)
  • [7] Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations
    Yi Hu
    Xiaochun Li
    The Journal of Geometric Analysis, 2015, 25 : 709 - 739
  • [8] Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations
    Hu, Yi
    Li, Xiaochun
    JOURNAL OF GEOMETRIC ANALYSIS, 2015, 25 (02) : 709 - 739
  • [9] Well-posedness of fully nonlinear KdV-type evolution equations
    Akhunov, Timur
    Ambrose, David M.
    Wright, J. Douglas
    NONLINEARITY, 2019, 32 (08) : 2914 - 2954
  • [10] 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
12345