Global existence and exponential stability for the micropolar fluid system

The existence and global exponential stability

Abstract By employing Schauder’s fixed point theorem and a non-Liapunov method (matrix theory, inequality analysis), we obtain some new criteria that ensure existence and global exponential stability of a periodic solution to a class of functional differential equations. Applying these criteria to a cellular neural network with time delays (delayed cellular neural network, DCNN) under a periodi...

Magneto-micropolar Fluid Motion: Global Existence of Strong Solutions

Here, u(t,x) ∈ R3 denotes the velocity of the fluid at a point x ∈ and time t ∈ [0,T ]; w(t,x) ∈ R3, b(t,x) ∈ R3 and p(t,x) ∈ R denote, respectively, the micro-rotational velocity, the magnetic field and the hydrostatic pressure; the constants μ,χ,α,β,γ,j , and ν are positive numbers associated to properties of the material; f (t,x), g(t,x) ∈ R3 are given external fields. We assume that on the ...

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability

Global Regularity Criterion for the Magneto-Micropolar Fluid Equations

ω(t, x) ∈ Rand b(t, x) ∈ R, and p(t, x) ∈ R denote, respectively, the microrotational velocity, the magnetic field, and the hydrostatic pressure. μ, χ, κ, γ, and ] are positive numbers associated with properties of the material: μ is the kinematic viscosity, χ is the vortex viscosity, κ and γ are spin viscosities, and 1/] is the magnetic Reynold. u 0 , ω 0 , and b 0 are initial data for the vel...

Exponential Stability and Global Attractors for a Thermoelastic Bresse System

We consider the stability properties for thermoelastic Bresse system which describes the motion of a linear planar shearable thermoelastic beam. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations...