Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222555 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 16 Pages |
Abstract
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 u0(x)
and satisfying the McKean condition, that is the quantity m0(x)=(1ââx2)u0(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)â¥Aâ1(1+C1Bt)â1exp{âC0âu0âH1t}, where A,B,C1 andC0 are suitable positive constants.
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Authors
A. Alexandrou Himonas, Gerson Petronilho,