The magneto-micropolar equations with periodic boundary conditions: solution properties at potential blow-up times
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.
scientific article; zbMATH DE number 6522707