Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations
نویسنده
چکیده
In this paper we study the magneto-micropolar fluid equations in R, prove the existence of the strong solution with initial data in H(R) for s > 3 2 , and set up its blow-up criterion. The tool we mainly use is Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda type blow-up criterion for smooth solution (u, ω, b) which relies on the vorticity of velocity ∇× u only.
منابع مشابه
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...
متن کاملLogarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.
متن کاملHALL AND LON-SLIP EFFECTS ON MAGNETO-MICROPOLAR FLUID WITH COMBINED FORCED AND FREE CONVECTION IN BOUNDARY LAYER FLOW OVER A HORIZONTAL PLATE WITH VISCOUS DISSIPATION
In this paper, we study the effects of Hall and ion-slip currents on the steady magneto-micropolar of a viscous incompressible and electrically conducting fluid over a horizontal plate by taking in to account the viscous dissipation effects. By means of similarity solutions, deviation of fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using qu...
متن کاملExistence theorem and blow - up criterion of the strong solutions to the two - fluid MHD equation in R 3
We first give the local well-posedness of strong solutions to the Cauchy problem of the 3D two-fluid MHD equations, and then study the blow-up criterion of the strong solutions. By means of the Fourier frequency localization and Bony’s paraproduct decomposition, it is proved that the strong solution (u, b) can be extended after t = T if either u ∈ LqT (Ḃ0 p,∞) with 2 q + 3 p ≤ 1 and b ∈ LT (Ḃ0 ...
متن کاملExistence theorem and blow - up criterion of strong solutions to the two - fluid MHD equation in R 3
We first give the local well-posedness of strong solutions to the Cauchy problem of 3D two-fluid MHD equations, then study the blow-up criterion of strong solutions. By means of the Fourier frequency localization and Bony’s paraproduct decomposition, it is proved that strong solution (u, b) can be extended after t = T if either u ∈ LqT (Ḃ 0 p,∞) with 2 q + 3 p ≤ 1 and b ∈ LT (Ḃ 0 ∞,∞), or (ω, J...
متن کامل