On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids

TL;DR

This paper proves the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids under certain initial conditions, extending understanding of the system's mathematical behavior.

Contribution

It establishes the global existence and uniqueness of 2D solutions for a regularized Rosensweig system with initial data in Sobolev spaces.

Findings

Solutions are globally defined for initial data in H^k with k ≥ 1.

The analysis applies to solutions with 2D initial data and magnetic fields.

The results contribute to the mathematical understanding of ferrofluid models.

Abstract

We study study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in $ H^k\left(\mathbb{R}^2\right), k\geqslant 1 $.