In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class for all and, as a consequence, the Hölder regularity of the solution . is an elliptic second order operator with discontinuous coefficients and the lower order terms belong to suitable Lebesgue spaces.
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.
In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, but depends on the growth properties of a certain function measuring some local potential of the weight.
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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