ANISOTROPIC GEVREY REGULARITY FOR MKDV ON THE CIRCLE

被引：0
作者：
Hannah, Heather [1 ]
Himonas, A. Alexandrou [2 ]
Petronilho, Gerson [3 ]
机构：
[1] E Cent Univ, Dept Math, Ada, OK 74820 USA
[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 31卷
基金：
巴西圣保罗研究基金会;
关键词：
Modified KdV equation; mKdV; Cauchy problem; periodic; Gevrey regularity; Sobolev spaces; GLOBAL WELL-POSEDNESS; DE-VRIES EQUATION; ILL-POSEDNESS; KDV; ANALYTICITY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that the solution to the Cauchy problem for the modified Korteweg de Vries equation with initial data in an analytic Gevrey space G(sigma), sigma >= 1, as a function of the spacial variable belongs to the same Gevrey space. However, considered as function of time the solution does not belong to G(sigma). In fact, it belong to G(3 sigma) and not to any Gevrey space G(r), 1 <= r < 3 sigma.
引用
收藏
页码：634 / 642
页数：9
相关论文
共 20 条
  • [1] [Anonymous], 2006, CBMS REGIONAL SERIES
  • [2] Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
    Bona, JL
    Grujic, Z
    Kalisch, H
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (06): : 783 - 797
  • [3] Bourgain J., 1993, The KdV equations, GAGA, V3, P209, DOI 10.1007/BF01895688
  • [4] Christ M, 2003, AM J MATH, V125, P1235
  • [5] Sharp global well-posedness for KDV and modified KDV on R and T
    Colliander, J
    Keel, M
    Staffilani, G
    Takaoka, H
    Tao, T
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 16 (03) : 705 - 749
  • [6] DEBOUARD A, 1995, ANN I H POINCARE-AN, V12, P673
  • [7] UNIQUENESS OF SOLUTIONS FOR THE GENERALIZED KORTEWEG-DEVRIES EQUATION
    GINIBRE, J
    TSUTSUMI, Y
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (06) : 1388 - 1425
  • [8] Gorsky J, 2005, CONTEMP MATH, V368, P233
  • [9] Construction of non-analytic solutions for the generalized KdV equation
    Gorsky, J
    Himonas, AA
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) : 522 - 529
  • [10] Grujie Z., 2002, Diff. Inte. Equ, V15, P1325
12