On the Cauchy Problem for the Fractional Camassa-Holm Equation

Nilay Duruk Mutlubas

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arXiv · 1807.04102

On the Cauchy Problem for the Fractional Camassa-Holm Equation

Nilay Duruk Mutlubas

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

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Nilay Duruk Mutlubas. 2018-07-11. On the Cauchy Problem for the Fractional Camassa-Holm Equation. https://arxiv.org/abs/1807.04102

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