Nonuniform Dependence of a Two-Component NOVIKOV System in Besov Spaces

Considered herein is the Cauchy problem of two-component Novikov system. In periodic case, we first constructed an approximate solution sequence that possesses nonuniform dependence property; then, by applying energy methods, managed to prove difference between and actual negligible, thus succeeding in proving result both supercritical Besov spaces Bp,rs(T)×Bp,rs(T) with s>max{32,1+1p},1≤p≤∞,1≤r<∞ critical space B2,132(T)×B2,132(T). non-periodic two sequences initial data high low-frequency terms analyzing inner structure system under investigation detail, proved distance corresponding lower-bounded time t, but converges zero at time. This implies map not uniformly continuous Bp,rs(R)×Bp,rs(R) Bp,11+1p(R)×Bp,11+1p(R) 1≤p≤2. The proof based on solutions Littlewood–Paley decomposition theory. These approaches are widely applicable study properties for shallow water equations.