Abstract
We prove the global existence strong solutions for the system of partial differential equations corresponding to the Shliomis model for magnetic fluids in exterior domains without regularization terms in the magnetization equation under the assumption of small data and also small coupling parameter.
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Notes
- $$ \int_{\varOmega }\nabla ( \mathbf{v}\cdot \nabla \mathbf{M} ) : \nabla \mathbf{M} dx= \int_{\varOmega }\nabla \mathbf{v}:\nabla \mathbf{M}\cdot \nabla \mathbf{M} dx dx\leq C \|\mathbf{v}\|_{1,2} \|\mathbf{M} \|_{2,2}^{2}.$$
\(\operatorname{{curl}}(m \times h)=m \operatorname{div} h-h \operatorname{div} m+(h\cdot \nabla )m-(m\cdot \nabla )h\).
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Acknowledgements
The author would like to thank Professor Giovanni P. Galdi for valuable comments and suggestions.
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Oliveira, J.C. Strong Solutions for Ferrofluid Equations in Exterior Domains. Acta Appl Math 156, 1–14 (2018). https://doi.org/10.1007/s10440-017-0152-z
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DOI: https://doi.org/10.1007/s10440-017-0152-z