scholarly journals Global strong solution and exponential decay for nonhomogeneous magnetohydrodynamic equations

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Xin Zhong ◽  
Keyword(s):  
Strong Solution ◽  
Exponential Decay ◽  
Magnetohydrodynamic Equations ◽  
Global Strong Solution

scholarly journals Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yong Zhou ◽  
Jishan Fan ◽  
Gen Nakamura
Keyword(s):  
Strong Solution ◽  
Initial Density ◽  
Regularity Criterion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Density Dependent ◽  
Global Strong Solution ◽  
Dependent Flow ◽  
Density Dependent Flow ◽  
Initial Boundary Value

The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocityu0and small∇d0. We also give a regularity criterion∇d∈Lp(0,T;Lq(Ω))  (2/q)+(2/p)=1, 2<q≤∞of the problem with the Dirichlet boundary conditionu=0,d=d0on∂Ω.

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