On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces

Jinlu Li; Yanghai Yu; Weipeng Zhu

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arXiv · 2304.11428

On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces

Jinlu Li·Yanghai Yu·Weipeng Zhu

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Abstract

In this paper we study the Cauchy problem of the Novikov equation in $\mathbb{R}$ for initial data belonging to the Triebel-Lizorkin spaces, i.e, $u_0\in F^{s}_{p,r}$ with $1< p, r<\infty$ and $s>\max\{\frac32,1+\frac1p\}$. We prove local-in-time unique existence of solution to the Novikov equation in $F^{s}_{p,r}$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in the same space.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2023-04-22. On the well-posedness and non-uniform continuous dependence for the Novikov equation in the Triebel-Lizorkin spaces. https://arxiv.org/abs/2304.11428

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