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

2018/04/18 by De Anna, Francesco, Scrobogna, Stefano
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.06619

Abstract

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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