Consider the Navier-Stokes equation with the initial data . Let and be two weak solutions with the same initial value . If satisfies the usual energy inequality and if where is the multiplier space, then we have .
A regularity criterion for strong solutions of the Ericksen-Leslie equations is established in terms of both the pressure and orientation field in homogeneous multiplier spaces.
We prove a regularity criterion for micropolar fluid flows in terms of one partial derivative of the velocity in a Morrey-Campanato space.
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65. We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
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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