Non-uniform continuous dependence on initial data for a two_component Novikov system in Besov space

TL;DR

This paper demonstrates that the solution map for a two-component Novikov system is not uniformly continuous in Besov spaces, extending previous results from Sobolev spaces and highlighting the system's sensitive dependence on initial data.

Contribution

It extends the non-uniform continuity results of the solution map from Sobolev spaces to Besov spaces for the two-component Novikov system.

Findings

Solution map is not uniformly continuous in Besov spaces

Extension of non-uniform dependence results from Sobolev to Besov spaces

Applicable for a range of parameters in Besov space settings

Abstract

In this paper, we show that the solution map of the two-component Novikov system is not uniformly continuous on the initial data in Besov spaces $B_{p, r}^{s-1}(\mathbb{R})\times B_{p, r}^s(\mathbb{R})$ with $s>\max\{1+\frac{1}{p}, \frac{3}{2}\}$, $1\leq p< \infty$, $1\leq r<\infty$. Our result covers and extends the previous non-uniform continuity in Sobolev spaces $H^{s-1}(\mathbb{R})\times H^s(\mathbb{R})$ for $s>\frac{5}{2}$ (J. Math. Phys., 2017) to Besov spaces.