Local and global analyticity for $\mu$-Camassa-Holm equations

Hideshi Yamane

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arXiv · 1906.11411

Local and global analyticity for $\mu$-Camassa-Holm equations

Hideshi Yamane

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Abstract

We solve Cauchy problems for some $\mu$-Camassa-Holm integro-partial differential equations in the analytic category. The equations to be considered are $\mu$CH of Khesin-Lenells-Misio\l{}ek, $\mu$DP of Lenells-Misio\l{}ek-Ti\u{g}lay, the higher-order $\mu$CH of Wang-Li-Qiao and the non-quasilinear version of Qu-Fu-Liu. We prove the unique local solvability of the Cauchy problems and provide an estimate of the lifespan of the solutions. Moreover, we show the existence of a unique global-in-time analytic solution for $\mu$CH, $\mu$DP and the higher-order $\mu$CH. The present work is the first result of such a global nature for these equations. AMS subject classification: 35R09, 35A01, 35A10, 35G25

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Hideshi Yamane. 2019-06-27. Local and global analyticity for $\mu$-Camassa-Holm equations. https://arxiv.org/abs/1906.11411

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