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Blow up criterion of smooth solutions to the MHD equations in Besov spaces. (English) Zbl 1081.35091

Summary: We discuss logarithmic Sobolev inequalities in Besov spaces, and show their applications to the blow up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.

MSC:

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
26D10 Inequalities involving derivatives and differential and integral operators
35B40 Asymptotic behavior of solutions to PDEs
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