Mathematics > Analysis of PDEs
[Submitted on 18 Apr 2018]
Title:A global well-posedness result for the Rosensweig system of ferrofluids
View PDFAbstract: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 solutions à la Leray of this model in the whole bidimensional space. Interesting enough, the well-posedness relies on a variation of the Aubin-Lions lemma for fractional time derivatives. 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
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