A new blowup criterion for strong solutions to the three-dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain

2017 ◽  
Vol 40 (15) ◽  
pp. 5526-5538 ◽  
Author(s):  
Yingshan Chen ◽  
Xiaofeng Hou ◽  
Limei Zhu
Keyword(s):  
Bounded Domain ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Magnetohydrodynamic Equations ◽  
Blowup Criterion

A BLOW-UP CRITERION FOR 3D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM

2012 ◽  
Vol 22 (02) ◽  
pp. 1150010 ◽  
Author(s):  
XINYING XU ◽  
JIANWEN ZHANG
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Magnetohydrodynamic Equations ◽  
The Cauchy Problem ◽  
Blow Up Criterion

This paper is concerned with a blow-up criterion of strong solutions for three-dimensional compressible isentropic magnetohydrodynamic equations with vacuum. It is shown that if the density and velocity satisfy [Formula: see text], where [Formula: see text], 3 < r ≤ ∞ and [Formula: see text] denotes the weak Lr-space, then the strong solutions to the Cauchy problem of the compressible magnetohydrodynamic equations can exist globally over [0, T].

scholarly journals Unique strong solutions and V-attractor of a three dimensional globally modified magnetohydrodynamic equations

2020 ◽  
Vol 19 (3) ◽  
pp. 1509-1535
Author(s):  
G. Deugoué ◽  
◽  
J. K. Djoko ◽  
A. C. Fouape ◽  
A. Ndongmo Ngana ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Strong Solutions ◽  
Magnetohydrodynamic Equations

scholarly journals Global Existence of Strong Solutions for Beris–Edwards’s Liquid Crystal System in Dimension Three

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 972
Author(s):  
Luo ◽  
Li ◽  
Zhao
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Global Existence ◽  
Evolution Equation ◽  
Bounded Domain ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupling System ◽  
Liquid Crystal System

We consider a system, established by Beris and Edwards in the Q-tensor framework,modeling the incompressible flow of nematic liquid crystals. The coupling system consists of theNavier–Stokes equation and the evolution equation for the Q-tensor. We prove the global existenceof strong solutions in a three-dimensional bounded domain with homogeneous Dirichlet boundaryconditions, under the assumption that the viscosity is sufficiently large.

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