scholarly journals Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation

2016 ◽  
Vol 260 (8) ◽  
pp. 6716-6744 ◽  
Author(s):  
Zhuan Ye ◽  
Xiaojing Xu
Keyword(s):  
Fractional Laplacian ◽  
Boussinesq Equations ◽  
Well Posedness ◽  
2D Boussinesq Equations

Finite-Dimensionality and Determining Modes of the Global Attractor for 2D Boussinesq Equations with Fractional Laplacian

2018 ◽  
Vol 18 (3) ◽  
pp. 501-515 ◽  
Author(s):  
Aimin Huang ◽  
Wenru Huo ◽  
Michael Jolly
Keyword(s):  
Global Attractor ◽  
Fractional Laplacian ◽  
Boussinesq Equations ◽  
Boussinesq System ◽  
Periodic Domain ◽  
Subcritical Case ◽  
Determining Modes ◽  
2D Boussinesq Equations ◽  
Finite Dimensionality

AbstractWe prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic domain with fractional Laplacian in the subcritical case.

scholarly journals Persistence of global well-posedness for the 2D Boussinesq equations with fractional dissipation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xing Su ◽  
Gangwei Wang ◽  
Yue Wang
Keyword(s):  
Sobolev Spaces ◽  
Strong Solutions ◽  
Boussinesq Equations ◽  
Well Posedness ◽  
Time Decay ◽  
Subcritical Case ◽  
2D Boussinesq Equations ◽  
Long Time

Abstract In this paper, we study the IBVP for the 2D Boussinesq equations with fractional dissipation in the subcritical case, and prove the persistence of global well-posedness of strong solutions. Moreover, we also prove the long time decay of the solutions, and investigate the existence of the solutions in Sobolev spaces $W^{2,p}({R}^{2})\times W^{1,p}({R}^{2})$ W 2 , p ( R 2 ) × W 1 , p ( R 2 ) for some $p>2$ p > 2 .

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