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On the Cauchy problem for the fractional Camassa–Holm equation

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Abstract

In this paper, we consider the Cauchy problem for the fractional Camassa–Holm equation which models the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. Using Kato’s semigroup approach for quasilinear evolution equations, we prove that the Cauchy problem is locally well-posed for data in \(H^{s}({\mathbb {R}})\), \(s>{\frac{5}{2}}\).

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Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Sabancı University, Orta Mahalle, 34956, Tuzla, Istanbul, Turkey

    N. Duruk Mutlubaş

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  1. N. Duruk Mutlubaş
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Correspondence to N. Duruk Mutlubaş.

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Communicated by A. Constantin.

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Mutlubaş, N.D. On the Cauchy problem for the fractional Camassa–Holm equation. Monatsh Math 190, 755–768 (2019). https://doi.org/10.1007/s00605-019-01278-6

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