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On global existence, energy decay and blow-up criteria for the Hall-MHD system. (English) Zbl 1328.35185
In this article the authors study the 3D incompressible Hall-Magnetohydrodynamics system. They show global existence of a unique solution in homogeneous Sobolev or Besov framework for small data together with various time decay properties of the solution. They also give two “Osgood type” blow-up criteria for local solutions on a finite interval $$(0,T_*)$$ when $$t\to T_*$$ and they finally prove two Beale-Kato-Majda criteria for local solutions of a related model.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 35B65 Smoothness and regularity of solutions to PDEs 76W05 Magnetohydrodynamics and electrohydrodynamics
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##### References:
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