scholarly journals A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain

2019 ◽  
Vol 64 (4) ◽  
pp. 397-407
Author(s):  
Jishan Fan ◽  
Xuanji Jia ◽  
Yong Zhou
Keyword(s):  
Bounded Domain ◽  
Stokes System ◽  
Regularity Criterion ◽  
Navier Stokes

Splitting-up scheme for the stochastic Cahn–Hilliard Navier–Stokes model

2020 ◽  
Vol 21 (01) ◽  
pp. 2150005
Author(s):  
Gabriel Deugoue ◽  
Boris Jidjou Moghomye ◽  
Theodore Tachim Medjo
Keyword(s):  
Bounded Domain ◽  
Stokes System ◽  
Navier Stokes ◽  
Binary Fluids ◽  
Martingale Solution ◽  
System Models ◽  
Compactness Method ◽  
External Forces

In this paper, we consider a stochastic Cahn–Hilliard Navier–Stokes system in a bounded domain of [Formula: see text] [Formula: see text]. The system models the evolution of an incompressible isothermal mixture of binary fluids under the influence of stochastic external forces. We prove the existence of a global weak martingale solution. The proof is based on the splitting-up method as well as some compactness method.

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