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Abstract:
In this paper we derive some new equations and we call them MHD-Leray-alpha equations which are similar to the MHD equations. We put forward the concept of weak and strong solutions for the new equations. Whether the 3-dimensional MHD equations have a unique weak solution is unknown, however, there is a unique weak solution for the 3-dimensional MHD-Leray-alpha equations. The global existence of strong solution and the Gevrey class regularity for the new equations are also obtained. Furthermore, we prove that the solutions of the MHD-Leray-alpha equations converge to the solution of the MHD equations in the weak sense as the parameter epsilon in the new equations converges to zero. (c) 2006 Elsevier Inc. All rights reserved.
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Source :
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN: 0022-247X
Year: 2007
Issue: 1
Volume: 329
Page: 298-326
0 . 8 7 2
JCR@2007
1 . 2 2 0
JCR@2019
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
CAS Journal Grade:2
Cited Count:
WoS CC Cited Count: 7
SCOPUS Cited Count: 9
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1