scholarly journals Global Solutions of 3-D Navier–Stokes System with Small Unidirectional Derivative

2019 ◽  
Vol 235 (2) ◽  
pp. 1405-1444 ◽  
Author(s):  
Yanlin Liu ◽  
Ping Zhang
Keyword(s):  
Stokes System ◽  
Global Solutions ◽  
Navier Stokes

scholarly journals Long-time behavior of global weak solutions for a Beris-Edwards type model of nematic liquid crystals

2020 ◽  
Author(s):  
Blanca CLIMENT-EZQUERRA ◽  
Francisco Guillen-Gonzalez
Keyword(s):  
Liquid Crystal ◽  
Stokes System ◽  
System Modeling ◽  
Fluid Velocity ◽  
Global Solutions ◽  
Navier Stokes ◽  
Type Model ◽  
Time Behavior ◽  
Infinite Time ◽  
Long Time

We consider a generalization of the standard Beris-Edwards system modeling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with an evolution equation for the Q-tensors variable describing the direction of liquid crystal molecules. The convergence at infinite time for global solutions is studied and we prove that whole trajectory goes to a single equilibrium by using a Lojasiewicz-Simon’s result.

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