J. Q. Yang (2019) established a regularity criterion for the 3D shear thinning fluids in the whole space via two velocity components. The goal of this short note is to extend this result in viewpoint of Lorentz space.
We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a large initial perturbation.
In this paper, the Cauchy problem for the Leray--MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray--MHD model in terms of the magnetic field only in the framework of homogeneous Besov space with negative index.
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