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.

中文翻译：

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罗森韦格铁磁流体系统的整体适定性结果

在本文中，我们研究了用于铁磁流体的Rosensweig系统的Bloch-Torrey正则化。本文的范围是双重的。首先，我们研究在整个空间$ \ mathbb R ^ 2 $中，该模型的Leray-Hopf解的存在性和唯一性。

在本文的第二部分中，我们研究了弱解的长期行为以及二维中Sobolev正则的传播。