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Logarithmically improved regularity criteria for the 3D viscous MHD equations. (English) Zbl 1247.35115

Summary: Various logarithmically improved regularity criteria for the 3D MHD equations are established in terms of the velocity field and pressure respectively. These regularity criteria can be regarded as log in time improvements of the standard Serrin’s criteria established before [C. He and Z. Xin, J. Differ. Equations 213, No. 2, 235–254 (2005; Zbl 1072.35154); Y. Zhou, Discrete Contin. Dyn. Syst. 12, No. 5, 881–886 (2005; Zbl 1068.35117)].

MSC:

35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

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[2] DOI: 10.1007/s00220-008-0545-y · Zbl 1168.35035 · doi:10.1007/s00220-008-0545-y
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