On the Cauchy Problem for the Fractional Camassa-Holm Equation

2018/07/11 by Mutlubas, Nilay Duruk · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.04102

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>(5)/(2).

Cited by

• On the Long Time Existence of a Fractional KdV-BBM Type Equation
• A convergent Fourier spectral Galerkin method for the fractional Camassa-Holm equation

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