On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipation

2015 ◽  
Vol 56 (5) ◽  
pp. 051504 ◽  
Author(s):  
Minggang Fei ◽  
Zhaoyin Xiang
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Small Data ◽  
Blow Up Criterion

scholarly journals Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up

2021 ◽  
Vol 7 (1) ◽  
pp. 247-257
Author(s):  
Jincheng Shi ◽  
◽  
Yan Zhang ◽  
Zihan Cai ◽  
Yan Liu ◽  
...  
Keyword(s):  
Global Existence ◽  
Nonlinear Problem ◽  
Weak Solutions ◽  
Blow Up ◽  
Small Data ◽  
Estimates Of Solutions ◽  
Derivative Type

<abstract><p>In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type $ |u_t|^p $. We demonstrate global existence of small data solutions if $ p &gt; 1+4/n $ ($ n\leq 6 $) or $ p\geq 2-2/n $ ($ n\geq 7 $), and blow-up of nontrivial weak solutions if $ 1 &lt; p\leq 1+1/n $. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>.</p></abstract>

scholarly journals Notes on the Global Well-Posedness for the Maxwell-Navier-Stokes System

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ensil Kang ◽  
Jihoon Lee
Keyword(s):  
Global Existence ◽  
Stokes System ◽  
Blow Up ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Well Posedness ◽  
Regular Solutions ◽  
2D System ◽  
Blow Up Criterion

Masmoudi (2010) obtained global well-posedness for 2D Maxwell-Navier-Stokes system. In this paper, we reprove global existence of regular solutions to the 2D system by using energy estimates and Brezis-Gallouet inequality. Also we obtain a blow-up criterion for solutions to 3D Maxwell-Navier-Stokes system.

scholarly journals On the blow-up criterion for the Hall-MHD problem with partial dissipation in R^3

2021 ◽  
Author(s):  
Baoying Du
Keyword(s):  
Blow Up ◽  
Global Solutions ◽  
Small Data ◽  
Partial Dissipation ◽  
Hall Mhd ◽  
Blow Up Criterion

We deal with the incompressible 3D Hall-magnetohydrodynamics with partial dissipation, a new blow-up criterion is obtained, based on which we also prove a new global solutions with small data.

Local existence and blow-up criterion for the Boussinesq equations

1997 ◽  
Vol 127 (5) ◽  
pp. 935-946 ◽  
Author(s):  
Dongho Chae ◽  
Hee-Seok Nam
Keyword(s):  
Global Existence ◽  
External Force ◽  
Existence And Uniqueness ◽  
Blow Up ◽  
Local Existence ◽  
Boussinesq Equations ◽  
Passive Scalar ◽  
Smooth Solutions ◽  
Local Existence And Uniqueness ◽  
Blow Up Criterion

SynopsisIn this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.

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