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VOL. 81 | 2019 Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons
Felipe Linares, Gustavo Ponce, Thomas C. Sideris

Editor(s) Keiichi Kato, Takayoshi Ogawa, Tohru Ozawa

Abstract

We shall study special properties of solutions to the IVP associated to the Camassa-Holm equation on the line related to the regularity and the decay of solutions. The first aim is to show how the regularity on the initial data is transferred to the corresponding solution in a class containing the “peakon solutions”. In particular, we shall show that the local regularity is similar to that exhibited by the solution of the inviscid Burger's equation with the same initial datum. The second goal is to prove that the decay results obtained in [17] extend to the class of solutions considered here.

Information

Published: 1 January 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07176822

Digital Object Identifier: 10.2969/aspm/08110197

Subjects:
Primary: 35Q51, 37K10

Rights: Copyright © 2019 Mathematical Society of Japan

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