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arXiv · 2309.15443

On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation

Nesibe Ayhan·Nilay Duruk Mutlubas
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Abstract

In this paper, we establish local well-posedness of the Cauchy problem for a recently proposed dispersion generalized Camassa-Holm equation by using Kato's semigroup approach for quasi-linear evolution equations. We show that for initial data in the Sobolev space $H^{s}(\mathbb{R})$ with $s>\frac{7}{2}+p$, the Cauchy problem is locally well-posed, where $p$ is an even real number determined by the order of the positive differential operator $L$ corresponding to the dispersive effect added to the Camassa-Holm equation.

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Nesibe Ayhan, Nilay Duruk Mutlubas. 2023-09-27. On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation. https://arxiv.org/abs/2309.15443

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