The magneto-micropolar equations with periodic boundary conditions: solution properties at potential blow-up times
type: Item
instance of: scholarly article
title: The magneto-micropolar equations with periodic boundary conditions: solution properties at potential blow-up times
zbMATH Open document ID: 1334.35248
author: Wilberclay G. Melo
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-12-21T00:00:00Z
review text: The magneto-micropolar system -- given in equations (1) -- reduces to the Navier-Stokes equations when the vortex viscosity, the micro-rotational velocity and the magnetic field are zero. When only the magnetic filed is zero, the magnetic-micropolar system becomes the micropolar system. In some previous papers cited by the author, were obtained lower bounds for the Navier-Stokes solutions, related with the blow-up time. These results were extended from the Navier-Stokes equations to the micropolar equations for incompressible flows. In the present paper, the author extends these last results to the case of magnetic-micropolar fluids on the torus in \(\mathbb R^3\). The lower estimates of the strong solutions at the potential blow-up time are obtained. The main tools are the homogeneous Sobolev spaces (defined by using the Fourier transform) and the interpolation inequalities.
reviewed by: Gelu Paşa
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 6522707
zbMATH Keywords: magneto-micropolar equations
zbMATH Keywords: blow-up criteria
zbMATH Keywords: homogeneous Sobolev spaces
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.11.005
OpenAlex ID: W2112282411
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cites work: Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations
DOI: 10.1016/J.JMAA.2015.11.005
description: scientific article; zbMATH DE number 6522707