scholarly journals Continuation Criterion for the 2D Liquid Crystal Flows

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Stokes System ◽  
Blow Up ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Sobolev Inequalities ◽  
Wave Maps ◽  
Logarithmic Sobolev Inequalities ◽  
Blow Up Criterion

We consider the 2D liquid crystal systems, which consists of Navier-Stokes system coupled with wave maps or biharmonic wave maps, respectively. By logarithmic Sobolev inequalities, we obtain a blow-up criterion ∇d,∂td∈L1(0,T;B˙∞,∞0(ℝ2)) for the case with wave maps, and we prove the existence of a global-in-time strong solutions for the case with biharmonic wave maps.

scholarly journals Notes on the Global Well-Posedness for the Maxwell-Navier-Stokes System

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ensil Kang ◽  
Jihoon Lee
Keyword(s):  
Global Existence ◽  
Stokes System ◽  
Blow Up ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Well Posedness ◽  
Regular Solutions ◽  
2D System ◽  
Blow Up Criterion

Masmoudi (2010) obtained global well-posedness for 2D Maxwell-Navier-Stokes system. In this paper, we reprove global existence of regular solutions to the 2D system by using energy estimates and Brezis-Gallouet inequality. Also we obtain a blow-up criterion for solutions to 3D Maxwell-Navier-Stokes system.

scholarly journals Regularity Criteria for a Coupled Navier-Stokes and Q-Tensor System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Stokes System ◽  
Type System ◽  
Parabolic Type ◽  
Strong Solutions ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Liquid Crystal Flow ◽  
Local Strong Solutions

We study a system describing the evolution of a nematic liquid crystal flow. The system couples a forced Navier-Stokes system describing the flow with a parabolic-type system describing the evolution of the nematic crystal director fields (Q-tensors). We prove some regularity criteria for the local strong solutions. However, we do not provide estimates on the rates of increase of high norms.

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