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

Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with the Navier-Stokes fluid

2019 ◽  
Vol 267 (9) ◽  
pp. 5410-5492
Author(s):  
Hideo Kozono ◽  
Masanari Miura ◽  
Yoshie Sugiyama
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Blow Up ◽  
Navier Stokes ◽  
Stokes Fluid ◽  
Blow Up Criterion

Blow-up and Global Smooth Solutions for Incompressible Three-Dimensional Navier–Stokes Equations

2008 ◽  
Vol 25 (6) ◽  
pp. 2115-2117 ◽  
Author(s):  
Guo Bo-Ling ◽  
Yang Gan-Shan ◽  
Pu Xue-Ke
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions

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.

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

scholarly journals A Beale–Kato–Majda blow-up criterion for the 3-D compressible Navier–Stokes equations

2011 ◽  
Vol 95 (1) ◽  
pp. 36-47 ◽  
Author(s):  
Yongzhong Sun ◽  
Chao Wang ◽  
Zhifei Zhang
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blow Up Criterion

Blow-up of smooth solutions to compressible quantum Navier-Stokes equations

2019 ◽  
Vol 50 (6) ◽  
pp. 873
Author(s):  
Dong Jianwei ◽  
Ju Qiangchang
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations

scholarly journals A blow-up criterion for classical solutions to the compressible Navier-Stokes equations

2010 ◽  
Vol 53 (3) ◽  
pp. 671-686 ◽  
Author(s):  
XiangDi Huang ◽  
ZhouPing Xin
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Navier Stokes Equations ◽  
Blow Up Criterion

Blow-up of smooth solutions to the Navier-Stokes-Poisson equations

2010 ◽  
Vol 34 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Huazhao Xie
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Poisson Equations
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