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Conservative solution of the Camassa Holm Equation on the real line

Massimo Fonte
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Abstract

In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan and the author constructed spatially periodic solutions, whereas in this paper the solutions are defined in all the real line. We introduce a distance functional, defined in terms of an optimal transportation problem, which allows us to study the continuous dependance w.r.t. the inital data with a certain decay at infinity.

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Massimo Fonte. 2005-11-22. Conservative solution of the Camassa Holm Equation on the real line. https://arxiv.org/abs/math/0511549

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