Abstract
In this paper, space-time regularity of the Koch and Tataru type solutions to MHD system was presented. More precisely, for the initial data \({(u_{0}, b_{0})\in {\it BMO}^{-1}}\), we shall present that the Koch and Tataru type solution of MHD equations (u,b) satisfying \({t^{m+{k/2}}(\partial_{t}^{m}\nabla^{k} u, \partial_{t}^{m}\nabla^{k} b)\in\mathbb{Z}_{\epsilon_0}}\) for any integers m, k ≥ 0, where \({\mathbb{Z}_{\epsilon_0}}\) is the Koch and Tataru (Adv Math 157:22–35, 2001) space. As a corollary, we also present the decay estimates.
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Du, Y. Space-time regularity of the solutions to MHD equations with small rough data. J. Evol. Equ. 15, 209–221 (2015). https://doi.org/10.1007/s00028-014-0256-0
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DOI: https://doi.org/10.1007/s00028-014-0256-0