Gevrey class regularity for solutions of micropolar fluid equations

Abstract

In this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class.

Ladder estimates for micropolar fluid equations and regularity of global attractor

“…Then we show that if the external fields have a cutoff in their spectra, the global attractor is made up form C ∞ functions. This result coincides with the result in [13], where it has been showed that if the external fields are in a Gevrey space of functions (have exponential decay of their Fourier spectra and so are analytic cf. i.e.…”

“…We treat it analogously to (13). As formerly to deal with the Laplacian term, we use (15), the fact that rot(rot ) =− +∇(div ) and (5)…”

“…Notice that the estimate of the nonlinear term is the same as in (13). The term including 4 r is integrated…”

Analysis of Pulsatile Blood Flow in an Elastic Artery Using the Cosserat Continuum Mechanical Approach

“…They assumed the artery's wall to be a rigid body and a solution to the Hagen-Poiseuilli flow of a micropolar fluid in an artery was obtained. Szopa [19] considered the solutions of micropolar fluid two-dimensional equations with periodic boundary condition.…”

Blow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosity

“…The existences of weak and strong solutions for micropolar fluid equations were treated by Galdi and Rionero [11] and Yamaguchi [12], respectively. The global regularity issue has been thoroughly investigated for the 3D micropolar fluid equations and many important regularity criteria have been established (see [13][14][15][16][17][18][19]). The convergence of weak solutions of the micropolar fluids in bounded domains of ℝ n was investigated (see [20]).…”