Strong solutions to the 2D Cauchy problem of density-dependent viscous Boussinesq equations with vacuum

2019 ◽  
Vol 60 (5) ◽  
pp. 051505 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Cauchy Problem ◽  
Strong Solutions ◽  
Boussinesq Equations ◽  
Density Dependent

scholarly journals The Cauchy problem and decay rates for strong solutions of a Boussinesq system

2005 ◽  
Vol 2005 (7) ◽  
pp. 757-766 ◽  
Author(s):  
Francisco Guillén González ◽  
Márcio Santos da Rocha ◽  
Marko Rojas Medar
Keyword(s):  
Heat Transfer ◽  
Cauchy Problem ◽  
Viscous Fluid ◽  
Strong Solutions ◽  
Boussinesq Equations ◽  
Decay Rates ◽  
Boussinesq System ◽  
Three Dimension ◽  
The Cauchy Problem ◽  
Derivatives Of

The Boussinesq equations describe the motion of an incompressible viscous fluid subject to convective heat transfer. Decay rates of derivatives of solutions of the three-dimension-al Cauchy problem for a Boussinesq system are studied in this work.

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.

Sign in / Sign up

Export Citation Format

Share Document