# On the cauchy problem for the fractional Camassa-Holm equation

Duruk Mutlubaş, Nilay (2019) On the cauchy problem for the fractional Camassa-Holm equation. Monatshefte für Mathematik . ISSN 0026-9255 (Print) 1436-5081 (Online) Published Online First http://dx.doi.org/10.1007/s00605-019-01278-6

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 $H^{s}({\Bbb R})$, $s>{\frac{5}{2}}$.