On the Cauchy problem of the two-component Novikov-type system with peaked solutions and H1-conservation law

Abstract

Considered herein is the Cauchy problem for the two-component Novikov-type system with peaked solutions and [Formula: see text]-conservation law. At first, we establish that the solutions maintain corresponding properties at infinity within the lifespan provided that the initial data decay exponentially and algebraically, respectively. Next, the local regularity and analyticity of the solutions to this problem in Sobolev–Gevrey spaces are discussed by a generalized Ovsyannikov theorem in detail.