Ill-posedness for a two-component Novikov system in Besov space

In this paper, we consider the Cauchy problem for a two-component Novikov system on the line. By specially constructed initial data (rho 0, u0) in Bs-1 p,infinity(R) x Bsp,infinity(R) with s >max{2 + p1,52 } and 1 < p< oo, we show that any energy bounded solution starting from (rho 0, u0) does not converge back to (rho 0, u0) in the metric of Bs-1 p,infinity(R) x Bsp,infinity(R) as time goes to zero, thus results in discontinuity of the data-to-solution map and ill-posedness.(c) 2023 Elsevier Inc. All rights reserved.