Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces

TL;DR

This paper establishes local existence and uniqueness of solutions for the non-resistive MHD equations within homogeneous Besov spaces, advancing mathematical understanding of these complex fluid dynamics equations.

Contribution

It introduces an improved proof of local existence and uniqueness using iterative schemes and compactness arguments, enhancing previous results.

Findings

Proved local existence of solutions in homogeneous Besov spaces.

Established uniqueness of solutions under certain conditions.

Improved upon recent mathematical results in the field.

Abstract

In the paper, we consider the Cauchy problem of the non-resistive MHD equations in homogeneous Besov spaces. We prove the local existence and uniqueness of the solution to the non-resistive MHD equations by using the iterative scheme and compactness arguments. Our obtained result improves considerably the recent results in \cite{C,W}.