scholarly journals On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data

2015 ◽  
Vol 32 (4) ◽  
pp. 813-832 ◽  
Author(s):  
Marius Paicu ◽  
Ping Zhang
Keyword(s):  
Stokes System ◽  
Global Solutions ◽  
Slow Variable ◽  
Navier Stokes ◽  
Density Dependent

scholarly journals Global large solutions to 3-D inhomogeneous Navier–Stokes system with one slow variable

2014 ◽  
Vol 256 (1) ◽  
pp. 223-252 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Marius Paicu ◽  
Ping Zhang
Keyword(s):  
Stokes System ◽  
Slow Variable ◽  
Navier Stokes ◽  
Large Solutions

Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system

2019 ◽  
Vol 16 (04) ◽  
pp. 701-742 ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Stokes System ◽  
Initial Density ◽  
Local Existence ◽  
Strong Solutions ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Initial Value ◽  
Two Phase ◽  
Density Dependent ◽  
Local Existence And Uniqueness

We study the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system, which describes a two-phase flow of two incompressible fluids with different densities. We establish the local existence and uniqueness of strong solutions to the initial value problem in a bounded domain, when the initial density function enjoys a positive lower bound.

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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