Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity

Global analytic solution in both the time and the space variables is proved for the Cauchy problem of a generalized CH equation, which contains as its members two integrable equations, namely the Camassa-Holm and the Novikov equations. The main assumptions are that the initial datum u(0)(x) is analytic on the line, it has uniform radius of analyticity r(0) > 0, and is such that the McKean quantity m(0)(x) = (1 - partial derivative(2)(x))u(0)(x) does not change sign. Furthermore, an explicit lower bound on the radius of space analyticity at later times is obtained, which is of the form L-3 exp(-L-1 exp(L-2t)), where L-1, L-2 and L-3 are appropriate positive constants. (C) 2017 Elsevier Inc. All rights reserved.