Local Well-Posedness and Blowup Criterion of the Boussinesq Equations in Critical Besov Spaces

2009 ◽  
Vol 12 (2) ◽  
pp. 280-292 ◽  
Author(s):  
Liu Xiaofeng ◽  
Meng Wang ◽  
Zhifei Zhang
Keyword(s):  
Besov Spaces ◽  
Boussinesq Equations ◽  
Well Posedness ◽  
Blowup Criterion ◽  
Critical Besov Spaces

scholarly journals The Well Posedness for Nonhomogeneous Boussinesq Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2110
Author(s):  
Yan Liu ◽  
Baiping Ouyang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Positive Constant ◽  
Besov Spaces ◽  
Initial Velocity ◽  
Initial Temperature ◽  
Boussinesq Equations ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Critical Besov Spaces

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces (θ,u)∈LT∞(B˙p,1N/p)×LT∞(B˙p,1N/p−1)⋂LT1(B˙p,1N/p+1) with 1<p<2N. We proved the global existence of the solution when the initial velocity is small with respect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, we proved the uniqueness for 1<p≤N. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations.

scholarly journals Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

2019 ◽  
Vol 60 (6) ◽  
pp. 061503
Author(s):  
Yuhui Chen ◽  
Wei Luo ◽  
Xiaoping Zhai
Keyword(s):  
Besov Spaces ◽  
Well Posedness ◽  
Critical Besov Spaces
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