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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.