Analysis on a generalized two-component Novikov system

TL;DR

This paper investigates a generalized two-component Novikov system with weak dissipation, establishing local well-posedness, wave breaking conditions, and persistence properties of solutions in weighted spaces.

Contribution

It introduces a comprehensive analysis of the generalized system, including well-posedness, wave breaking criteria, and solution persistence in weighted function spaces.

Findings

Established local well-posedness using Kato's theorem

Derived necessary and sufficient conditions for wave breaking

Analyzed persistence of solutions in weighted $L^{p}$ spaces

Abstract

In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted $L^{p}(\mathbb{R})$ spaces for a large class of moderate weights.