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.

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 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
Sign in / Sign up

Export Citation Format

Share Document