A blow-up criterion for the smooth solutions to the Keller-Segel system coupled with the Navier-Stokes fluid

2021 ◽  
Vol 9 (1) ◽  
pp. 25-30
Author(s):  
Mingxue Zhang ◽  
Fuyi Xu
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Stokes Fluid ◽  
Blow Up Criterion

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