Abstract
This paper is devoted to the large time decay of solutions of a three-dimensional Stokes-Magneto equations. It is shown that, when initial data belong to \(L^2\), weak solutions of the equations decay to zero in \(L^{3/2,\infty }\times L^2\) without a uniform rate, and this decay estimate is optimal. Furthermore, the optimal temporal decay estimates for weak solutions are established when initial data belongs to \(L^1\cap L^2\).
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Acknowledgements
The authors would like to thank the referee for the carefully reading of the earlier version of the manuscript and insightful comments which greatly improved the scope of this paper. The first author was partially supported by NSFC Grant (#11701099), the second author was partially supported by Guangdong Basic and Applied Basic Research Foundation (#2020A1515110299).
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Ji, Y., Tan, W. Large time behavior of solutions to a Stokes-Magneto equations in three dimensions. J. Evol. Equ. 21, 2449–2470 (2021). https://doi.org/10.1007/s00028-021-00689-z
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DOI: https://doi.org/10.1007/s00028-021-00689-z