Micropolar Fluid Equations Research Articles

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some T > 0, if , where 3/ϱ + 2/ρ ≤ 1 and ϱ ≥ 3, then the solution (v, w) can be extended smoothly beyond t = T. The derivative can be substituted with any directional derivative of v.

Existence and uniqueness of strong solution for the incompressible micropolar fluid equations in domains of $${\mathbb{R}^3}$$

We consider the initial boundary value problem for the system of equations describing the nonstationary flow of an incompressible micropolar fluid in a domain Ω of \({\mathbb{R}^3}\). Under hypotheses that are similar to the Navier-Stokes equations, by using an iterative scheme, we prove the existence and uniqueness of strong solution in Lp(Ω), for p > 3.

On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space

On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space

Ladder estimates for micropolar fluid equations and regularity of global attractor

This paper is devoted to obtain ladder inequalities for 2D micropolar fluid equations on a periodic domain Q=(0, L)2. The ladder inequalities are differential inequalities that connect the evolution of L2 norms of derivatives of order N with the evolution of the L2 norms of derivatives of other (usually lower) order. Moreover, we find (with slight assumption on external fields) long-time upper bounds on the L2 norms of derivatives of every order, which implies that a global attractor is made up from C∞ functions. Copyright © 2010 John Wiley & Sons, Ltd.

On the Regularity for Solutions of the Micropolar Fluid Equations

We give sufficient conditions on the kinematics pressure in order to obtain regularity and uniqueness of the weak solutions to the micropolar fluid equations.

Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

Exact and numerical solutions of a micropolar fluid in a vertical annulus

AbstractIn this article, we have analyzed the effects of heat transfer on a peristaltic flow of a micropolar fluid in a vertical annulus. The governing equations of two‐dimensional micropolar fluid are simplified by using the assumptions of long wavelength and neglecting the wave number. A close form solutions are obtained for velocity field υx and microrotation component υθ. Further, the numerical solutions of the simplified equation of υθ are computed and the results are compared with the exact solution. The influence of pertinent parameters are analyzed through graphs. Trapping phenomena is also discussed for different parameters. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010

On H1-pullback attractors for nonautonomous micropolar fluid equations in a bounded domain

Using a method based on the concept of the Kuratowski measure of noncompactness of a bounded set as well as some new estimates of solutions we prove the existence of a unique minimal pullback attractor for the evolutionary process associated with nonautonomous two-dimensional micropolar fluid equations in a bounded domain, where the forces and moments satisfy only a certain integrability condition. In earlier similar research forces and moments were assumed to be uniformly bounded in time.

Gevrey class regularity for solutions of micropolar fluid equations

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.

On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations

The present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in R 2 . Upper and lower bounds are derived for the L 2 decay rates of higher order derivatives of solutions to the micropolar fluid flows. The findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized Gronwall type argument.

On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

AbstractIn this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.

Some properties of a class of abstract stationary equations

We study a class of abstract nonlinear equations in a separable Hilbert space for which we prove some generic properties of the set of solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar equations, micropolar fluid equations, Boussinesq and Navier–Stokes equations.

Basic Equations and Constitutive Equations of Micropolar Magnetic Fluids with E-B Analogy and the Abraham Expression of Electromagnetic Momentum

A complete set of basic equations for magnetic fluids with internal rotation is proposed in this paper. The basic equations are derived from the conservation laws of mass, linear momentum, angular momentum and energy, while the constitutive equations are obtained by the thermodynamical method that is based on the free energy and the dissipation function. The concrete expression of constitutive equations are determined by the principle of material frame indifference and the principle of maximal dissipation rate. The Abraham expression of the electromagnetic momentum and E-B analogy are adopted in this theory. It is shown that the difference in the basic equations in case of adopting the Abraham expression and the Minkowski expression, respectively. The constitutive equation of magnetization which includes the Shliomis relaxation equation (1972) is proposed.

Basic Equations of Micropolar Magnetic Fluids

A complete set of the basic equations for magnetic fluids with internal rotation is proposed in this paper. The basic equations and constitutive equations are derived by the thermodynamical method in which free energy and dissipation function are used on basis of the conservation laws. The balance equations are derived from the conservation laws of mass, momentum, angular momentum and energy. The constitutive equations such as the stress tensor, the coupled stress tensor, the magnetization are determined by the principle of maximal dissipation rate and the principle of material frame indifference. The constitutive equation of magnetization which includes Shliomis's relaxation equation is proposed.

Stationary micropolar fluid with boundary data in L2

We consider the Dirichlet boundary value problem for the equations of a stationary micropolar fluid in a bounded three-dimensional domain. We show the existence and uniqueness of a distributional solution with boundary values in L 2.

A spatial decay estimate of the flow equations of micropolar fluids

The equations of incompressible micropolar flow are a coupled system of vector differential equations involving the two basic vectors, viz. the velocity v ̄ and the microrotation v ̄ of the fluid elements. Let Ω 0 be a spatial domain which is bounded, in part, by a planar region Σ 0. An energytype functional of solutions of the flow equations of micropolar fluids is defined. It is shown that this functional decays exponentially in the distance from a fixed reference plane.

A note on the existence and uniqueness of solutions of the micropolar fluid equations

We show that existence and uniqueness theorems, known in the theory of the Navier-Stokes equations, are valid for the incompressible micropolar equations too.