Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations
نویسندگان
چکیده
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.
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Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity, η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. As same as the 3D Navier-Stokes equations, the regularity of ...
متن کاملOn the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space
In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space L(R). We obtain that if u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 1 with 3 < p ≤ ∞; or ∇u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or the pressure P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or ∇P ...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2011
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2011/456547