3-D stochastic micropolar and magneto-micropolar fluid systems with non-Lipschitz multiplicative noise

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...

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 ...

Stochastic reaction - diffusion systems with multiplicative noise and non - Lipschitz reaction term

We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains of R , perturbed by a multiplicative noise. The reaction term is assumed to have polynomial growth and to be locally Lipschitz-continuous and monotone. The noise is white in space and time if d = 1 and colour...

Theory and simulation of micropolar fluid dynamics

This paper reviews the fundamentals of micropolar fluid dynamics (MFD), and proposes a numerical scheme integrating Chorin’s projection method and time-centred split method (TCSM) for solving unsteady forms of MFD equations. It has been known that Navier–Stokes equations are incapable of explaining the phenomena at micro and nano scales. On the contrary, MFD can naturally pick up the physical p...

Regularity criteria for the 3D magneto-micropolar fluid equations in Besov spaces with negative indices