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

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, $u_0\in F_{p,r}^s$ with $1<p,r<\mathrm{\infty }$ and $s>\max \{\frac{3}{2},1+\frac{1}{p}\}$. We prove local-in-time unique existence of solution to the Novikov equation in $F_{p,r}^s$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in the same space.