Revista Matemática Iberoamericana

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Published online first: 2020-01-03
DOI: 10.4171/rmi/1153

A global well-posedness result for the Rosensweig system of ferrofluids

Francesco De Anna[1] and Stefano Scrobogna[2]

(1) Universität Würzburg, Germany
(2) Universidad de Sevilla, Spain

In this paper we study a Bloch–Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray–Hopf solutions of this model in the whole space $\mathbb R^2$.

In the second part of this paper we investigate both the long-time behavior of weak solutions and the propagation of Sobolev regularities in dimension two.

Keywords: Ferrofluids, fractional time derivative, global well-posedness, long time behavior, decay estimates, regularity propagation

De Anna Francesco, Scrobogna Stefano: A global well-posedness result for the Rosensweig system of ferrofluids. Rev. Mat. Iberoam. Electronically published on January 3, 2020. doi: 10.4171/rmi/1153 (to appear in print)