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http://dx.doi.org/10.12941/jksiam.2022.26.076

EXISTENCE AND DECAY PROPERTIES OF WEAK SOLUTIONS TO THE INHOMOGENEOUS HALL-MAGNETOHYDRODYNAMIC EQUATIONS  

HAN, PIGONG (ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE, CHINESE ACADEMY OF SCIENCES)
LEI, KEKE (ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE, CHINESE ACADEMY OF SCIENCES)
LIU, CHENGGANG (SCHOOL OF STATISTICS AND MATHEMATICS, ZHONGNAN UNIVERSITY OF ECONOMICS AND LAW)
WANG, XUEWEN (ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE, CHINESE ACADEMY OF SCIENCES)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.26, no.2, 2022 , pp. 76-107 More about this Journal
Abstract
In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded mollification technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.
Keywords
Hall-magnetohydrodynamic equations; weak solution; existence; decay;
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