scholarly journals A regularity criterion for the Cahn-Hilliard-Boussinesq system with zero viscosity

2014 ◽  
Vol 2014 (1) ◽  
pp. 287
Author(s):  
Caochuan Ma ◽  
Faris Alzahrani ◽  
Tasawar Hayat ◽  
Yong Zhou
Keyword(s):  
Regularity Criterion ◽  
Boussinesq System ◽  
Zero Viscosity

scholarly journals Blow-Up Criteria of Smooth Solutions for the Cahn-Hilliard-Boussinesq System with Zero Viscosity in a Bounded Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yong Zhou ◽  
Jishan Fan
Keyword(s):  
Bounded Domain ◽  
Smooth Solution ◽  
Blow Up ◽  
Boussinesq System ◽  
Smooth Solutions ◽  
Zero Viscosity

We prove that a smooth solution of the 3D Cahn-Hilliard-Boussinesq system with zero viscosity in a bounded domain breaks down if a certain norm of vorticity blows up at the same time. Here, this norm is weaker than bmo-norm.

On the Cauchy problems for certain Boussinesq-α equations

2010 ◽  
Vol 140 (2) ◽  
pp. 319-327 ◽  
Author(s):  
Yong Zhou ◽  
Jishan Fan
Keyword(s):  
Cauchy Problem ◽  
Smooth Solution ◽  
Boussinesq Equations ◽  
Regularity Criterion ◽  
Boussinesq System ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Boussinesq Systems

We study the Cauchy problem of certain Boussinesq-α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ▽u ∈ L1 (0, T; Ḃ0∞,∞(ℝn)). As a corollary, the smooth solution of the Leray-α–Boussinesq system exists globally, when n = 2. For the Lagrangian averaged Boussinesq equations, a regularity criterion ▽θ ∈ L1(0, T;L∞(ℝ2)) is established. Other Boussinesq systems with partial viscosity are also discussed in the paper.

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