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

A LOGARITHMALLY IMPROVED BLOW-UP CRITERION OF SMOOTH SOLUTIONS FOR THE THREE-DIMENSIONAL MHD EQUATIONS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250027 ◽  
Author(s):  
YU-ZHU WANG ◽  
HENGJUN ZHAO ◽  
YIN-XIA WANG
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Smooth Solutions ◽  
The Cauchy Problem ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Blow Up Criterion

In this paper we investigate the Cauchy problem for the three-dimensional incompressible magnetohydrodynamic equations. A logarithmal improved blow-up criterion of smooth solutions is obtained.

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.

On the Blow-Up Criterion for Incompressible Stokes–MHD Equations

2018 ◽  
Vol 73 (3) ◽  
Author(s):  
Ahmad Mohammad Alghamdi ◽  
Sadek Gala ◽  
Maria Alessandra Ragusa
Keyword(s):  
Blow Up ◽  
Mhd Equations ◽  
Blow Up Criterion

scholarly journals On the Well-Posedness of the Boussinesq Equation in the Triebel-Lizorkin-Lorentz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhaoyin Xiang ◽  
Wei Yan
Keyword(s):  
Boussinesq Equation ◽  
Blow Up ◽  
Boussinesq Equations ◽  
Lorentz Spaces ◽  
Well Posedness ◽  
Smooth Solutions ◽  
Blow Up Criterion

We establish the local well-posedness and obtain a blow-up criterion of smooth solutions for the Boussinesq equations in the framework of Triebel-Lizorkin-Lorentz spaces. The main ingredients of our proofs are Littlewood-Paley decomposition and the paradifferential calculus.

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