Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations
type: Item
instance of: scholarly article
title: Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations
zbMATH Open document ID: 1185.35201
author: Kaitai Li
author: Yong-Jiang Yu
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-26T00:00:00Z
review text: The authors derive some new equations which they call MHD-Leray-alpha equations, and which are similar to the MHD equations. For these equations, the authors prove the existence of a unique weak solution and a unique strong solution global in time. The authors also establish the Gevrey class of regularity when the initial data are smooth enough and the forces belong to a suitable Gevrey class. Moreover, it is shown that the solutions of the MHD-Leray-alpha equations converge to the solution of the MHD equations in a weak sense as a parameter in the new equations converges to zero. The proof is based on Faedo-Galerkin method and on Fourier series expansions.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 5129647
zbMATH Keywords: Navier--Stokes equations
zbMATH Keywords: MHD equations
zbMATH Keywords: MHD-Leray-alpha equations
zbMATH Keywords: weak solution
zbMATH Keywords: strong solution
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.06.039
OpenAlex ID: W2006279392
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DOI: 10.1016/J.JMAA.2006.06.039
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description: scientific article; zbMATH DE number 5129647