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arXiv · 1605.03218

Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics

Grzegorz Jamróz
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Abstract

We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to positive and negative slopes are one-sided weakly continuous and of bounded variation, which allows us to define certain measures of dissipation of both parts of energy. The result is a step towards the open problem of uniqueness of dissipative solutions of the Camassa-Holm equation.

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Grzegorz Jamróz. 2016-11-09. Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics. https://arxiv.org/abs/1605.03218

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