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

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 Bp,rs−1(R)×Bp,rs(R) with s>max{1+1p,32}, 1≤p≤∞, 1≤r<∞. Our result covers and extends the previous non-uniform continuity in Sobolev spaces Hs−1(R)×Hs(R) for s>52 to Besov spaces.