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Title of Journal: Acta Math Appl Sin Engl Ser

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Abbravation: Acta Mathematicae Applicatae Sinica, English Series

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Springer-Verlag

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10.1007/s00198-015-3170-6

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1618-3932

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Regularity criteria of axisymmetric weak solutions

Authors: Baoquan Yuan Fengping Li
Publish Date: 2013/04/10
Volume: 29, Issue: 2, Pages: 289-302
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Abstract

In this paper we study the regularity criteria for axisymmetric weak solutions to the MHD equations in ℝ3 Let ω θ J θ and u θ be the azimuthal component of ω J and u in the cylindrical coordinates respectively Then the axisymmetric weak solution u b is regular on 0 T if ω θ J θ ∈ L q 0 T L p or ω θ ▽u θ e θ ∈ L q 0 T L p with tfrac3 p + tfrac2 q leqslant 2 tfrac3 2 p infty In the endpoint case one needs conditions left omega theta J theta right in L1 left 0Tdot B infty infty 0 right or left omega theta nabla left u theta e theta right right in L1 left 0Tdot B infty infty 0 rightThe research of BQ Yuan was partially supported by the National Natural Science Foundation of China No 10771052 11071057 Program for Science Technology Innovation Talents in Universities of Henan Province No 2009HASTIT007 the Innovation Scientists and Technicians Troop Construction Projects of Henan Province No 104100510015 FP Li was supported by the young fund and excellent young teacher fund of Henan Polytechnic University No Q2011144 649177


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