Abstract
AbstractThis paper examines the existence and uniqueness of weak solutions to the d‐dimensional magnetohydrodynamic (MHD) equations with fractional dissipation and fractional magnetic diffusion . The aim is at the uniqueness of weak solutions in the weakest possible inhomogeneous Besov spaces. We establish the local existence and uniqueness in the functional setting and when , and . The case when with and has previously been studied in [7, 19]. However, their approaches can not be directly extended to the fractional case when due to the breakdown of a bilinear estimate. By decomposing the bilinear term into different frequencies, we are able to obtain a suitable upper bound on the bilinear term for , which allows us to close the estimates in the aforementioned Besov spaces.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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