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arXiv · 1804.06619

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

Francesco De Anna·Stefano Scrobogna
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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 \`a 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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Francesco De Anna, Stefano Scrobogna. 2018-04-18. A global well-posedness result for the Rosensweig system of ferrofluids. https://arxiv.org/abs/1804.06619

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