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arXiv · 1609.09176

Global conservative solution for the periodic $\mu$-Camassa-Holm equation

Wei Luo·Zhaoyang Yin
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Abstract

In this paper we mainly investigate the periodic $\mu$-Camassa-Holm equation. We show the existence of global conservative solutions to the Cauchy problem of the periodic $\mu$-Camassa-Holm equation. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Our solutions depend continuously on the initial data and has a semigroup property.

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Wei Luo, Zhaoyang Yin. 2016-09-29. Global conservative solution for the periodic $\mu$-Camassa-Holm equation. https://doi.org/10.1063/5.0048245

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