Blow-Up Criteria and Regularity Criterion for the Three-Dimensional Magnetic Bénard System in the Multiplier Space

2018 ◽  
Vol 73 (3) ◽  
Author(s):  
Liangliang Ma
Keyword(s):  
Blow Up ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Multiplier Space ◽  
Bénard System

scholarly journals A new blow up criterion for the 3D magneto-micropolar fluid flows without magnetic diffusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dongxiang Chen ◽  
Qifeng Liu
Keyword(s):  
Magnetic Field ◽  
Weak Solution ◽  
Micropolar Fluid ◽  
Blow Up ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Regularity Criterion ◽  
Gradient Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field

AbstractThis note obtains a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of one velocity component and the gradient field of the magnetic field. The authors prove that the weak solution $(u,\omega,b)$ ( u , ω , b ) to the magneto-micropolar fluid flows can be extended beyond time $t=T$ t = T , provided if $u_{3}\in L^{\beta }(0,T;L^{\alpha }(R^{3}))$ u 3 ∈ L β ( 0 , T ; L α ( R 3 ) ) with $\frac{2}{\beta }+\frac{3}{\alpha }\leq \frac{3}{4}+\frac{1}{2\alpha },\alpha > \frac{10}{3}$ 2 β + 3 α ≤ 3 4 + 1 2 α , α > 10 3 and $\nabla b\in L^{\frac{4p}{3(p-2)}}(0,T;\dot{M}_{p,q}(R^{3}))$ ∇ b ∈ L 4 p 3 ( p − 2 ) ( 0 , T ; M ˙ p , q ( R 3 ) ) with $1< q\leq p<\infty $ 1 < q ≤ p < ∞ and $p\geq 3$ p ≥ 3 .

SOME PERIODIC AND BLOW-UP SOLUTIONS FOR LANDAU–LIFSHITZ EQUATION

2011 ◽  
Vol 26 (32) ◽  
pp. 2437-2452 ◽  
Author(s):  
PENGHONG ZHONG ◽  
SHU WANG ◽  
SHENGTAO CHEN
Keyword(s):  
Exact Solution ◽  
Periodic Solution ◽  
Exact Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Three Dimensional ◽  
Ferromagnetic Materials ◽  
Lifshitz Equation ◽  
Dimensional Spacetime ◽  
Vortex Solution

In this paper, we construct the exact solution of two- or three-dimensional spacetime Landau–Lifshitz equation raised in the ferromagnetic materials. Under suitable transformations, some exact solutions are obtained in the radially symmetric coordinates and nonsymmetric coordinates. The type of solutions cover the finite time blow-up solution, vortex solution and periodic solution. In the end, we sketch some solutions and their spatial curvatures.

On regularity criteria of a weak solution to the three-dimensional magnetohydrodynamics equations in Lorentz space

2018 ◽  
Vol 148 (3) ◽  
pp. 593-604
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Weak Solution ◽  
Bounded Domain ◽  
Lorentz Space ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
Magnetohydrodynamics Equations

We give a weak-Lp Serrin-type regularity criterion for a weak solution to the three-dimensional magnetohydrodynamics equations in a bounded domain Ω ⊂ ℝ3.

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