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.

Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded domain

2012 ◽  
Vol 75 (7) ◽  
pp. 3436-3442 ◽  
Author(s):  
Jishan Fan ◽  
Gen Nakamura ◽  
Haibing Wang
Keyword(s):  
Bounded Domain ◽  
Blow Up ◽  
Boussinesq System ◽  
Smooth Solutions ◽  
Zero Viscosity

On the blow-up criterion for the 3D Boussinesq system with zero viscosity constant

2014 ◽  
Vol 94 (4) ◽  
pp. 856-862 ◽  
Author(s):  
Wei Ren
Keyword(s):  
Blow Up ◽  
Boussinesq System ◽  
Zero Viscosity ◽  
Blow Up Criterion

scholarly journals Some Blow-Up and Smooth Solutions about Landau-Lifshitz Equation and Their Spatial Curvature Behavior

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Penghong Zhong ◽  
Shu Wang ◽  
Ming Zeng
Keyword(s):  
Exact Solution ◽  
Finite Time ◽  
Smooth Solution ◽  
Blow Up ◽  
Dimensional Space ◽  
Smooth Solutions ◽  
Spatial Curvature ◽  
Lifshitz Equation ◽  
Vortex Solution ◽  
Dimensional Space Time

We construct the exact solution of (2+1)-dimensional space-time Landau-Lifshitz equation (LLE) without the Gilbert term. Under suitable transformations, some exact solutions are obtained in the radially symmetric coordinates and nonsymmetric coordinates. The type of solutions cover the finite-time blow-up solution, smooth solution in time and vortex solution. At the end, some properties about these solutions and their spatial curvature are illustrated by the graphs.

scholarly journals Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Jishan Fan ◽  
Wenjun Sun ◽  
Junping Yin
Keyword(s):  
Bounded Domain ◽  
Blow Up ◽  
Boussinesq System ◽  
Mhd System

scholarly journals On blow-up criteria of smooth solutions to the 3-D Euler equations in a bounded domain

2003 ◽  
Vol 190 (1) ◽  
pp. 39-63 ◽  
Author(s):  
Takayoshi Ogawa ◽  
Yasushi Taniuchi
Keyword(s):  
Euler Equations ◽  
Bounded Domain ◽  
Blow Up ◽  
Smooth Solutions

Blow-up and Global Smooth Solutions for Incompressible Three-Dimensional Navier–Stokes Equations

2008 ◽  
Vol 25 (6) ◽  
pp. 2115-2117 ◽  
Author(s):  
Guo Bo-Ling ◽  
Yang Gan-Shan ◽  
Pu Xue-Ke
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions

scholarly journals Blow-up criterion for the density dependent inviscid Boussinesq equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Li Li ◽  
Yanping Zhou
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Boussinesq Equations ◽  
Smooth Solutions ◽  
Density Dependent ◽  
Priori Estimates ◽  
Blow Up Criterion

Abstract In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in $\mathbb{R}^{N}\ (N\geq 2)$ R N ( N ≥ 2 ) . By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.

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

An improved blow-up criterion for smooth solutions of the two-dimensional MHD equations

2016 ◽  
Vol 40 (1) ◽  
pp. 279-285 ◽  
Author(s):  
Sadek Gala ◽  
Alessandra Maria Ragusa ◽  
Zhuan Ye
Keyword(s):  
Blow Up ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Smooth Solutions ◽  
Blow Up Criterion
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