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arXiv · 1801.03777

On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids

Stefano Scrobogna
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Abstract

We study study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in $ H^k\left(\mathbb{R}^2\right), k\geqslant 1 $.

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Stefano Scrobogna. 2018-01-11. On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids. https://arxiv.org/abs/1801.03777

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