Well-posedness of the two-component Fornberg-Whitham system in Besov spaces

TL;DR

This paper proves the well-posedness of the two-component Fornberg-Whitham system in Besov spaces, demonstrating existence, uniqueness, and continuous dependence of solutions on initial data within these function spaces.

Contribution

It establishes the well-posedness of the system in Besov spaces, a result not previously known for this model.

Findings

Existence and uniqueness of solutions in Besov spaces

Continuity of the data-to-solution map

Solutions depend continuously on initial data

Abstract

The present paper establishes well-posedness for the two-component Fornberg-Whitham system in Besov spaces. First the existence and uniqueness of its solution is proved, then it is shown that the corresponding data-to-solution map is continuous, provided the initial data belong to Besov spaces.