Ill-Posedness of a Three-Component Novikov System in Besov Spaces

Abstract

In this paper, we consider the Cauchy problem for a three-component Novikov system on the line. We give a construction of the initial data (ρ0,u0,v0)∈Bp,∞σ−1(R)×Bp,∞σ(R)×Bp,∞σ(R) with σ>max3+1p,72,1≤p≤∞, such that the corresponding solution to the three-component Novikov system starting from (ρ0,u0,v0) is discontinuous at t=0 in the metric of Bp,∞σ−1(R)×Bp,∞σ(R)×Bp,∞σ(R), which implies the ill-posedness for this system in Bp,∞σ−1(R)×Bp,∞σ(R)×Bp,∞σ(R).

Keywords

• ill-posedness
• three-component Novikov system
• Besov spaces