Radius of analyticity for the Camassa-Holm equation on the line

被引:4
作者
Himonas, A. Alexandrou [1 ]
Petronilho, Gerson [2 ]
机构
[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
基金
巴西圣保罗研究基金会;
关键词
Camassa-Holm equation; Cauchy problem; Analytic data; Global in time solutions; Analytic spaces; Exponential lower bound on the radius of analyticity; 3-DIMENSIONAL EULER EQUATIONS; TRAVELING-WAVE SOLUTIONS; SHALLOW-WATER EQUATION; SPATIAL ANALYTICITY; CAUCHY-PROBLEM; KDV EQUATION; PEAKON SOLUTIONS; LOWER BOUNDS; FAMILY; PERSISTENCE;
D O I
10.1016/j.na.2018.04.007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Using estimates in Sobolev spaces we prove that the solution to the Cauchy problem for the Camassa-Holm equation on the line with analytic initial data u(0)(x) and satisfying the McKean condition, that is the quantity m(0)(x) = (1 - (2)(partial derivative x))u(0)(x) does not change sign, is analytic in the spatial variable for all time. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity r(t) given by r(t) >= A(-1) (1 + C(1)Bt)(-1) exp{-C-0 parallel to u(0)parallel to(H1t)}, where A, B, C-1 and C-0 are suitable positive constants. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1 / 16
页数:16
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