scholarly journals Global well-posedness of the $ n $-dimensional hyper-dissipative Boussinesq system without thermal diffusivity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xuemin Deng ◽  
Yuelong Xiao ◽  
Aibin Zang
Keyword(s):  
Thermal Diffusivity ◽  
Boussinesq System ◽  
Well Posedness

Global Well-Posedness and Convergence Results for the 3D-Regularized Boussinesq System

2012 ◽  
Vol 64 (6) ◽  
pp. 1415-1435 ◽  
Author(s):  
Ridha Selmi
Keyword(s):  
Existence And Uniqueness ◽  
Analytical Study ◽  
Approximation Scheme ◽  
Boussinesq System ◽  
Well Posedness ◽  
Energy Methods ◽  
Unique Weak Solution ◽  
Frequency Space ◽  
Convergence Results ◽  
Fourier Theory

Abstract Analytical study of the regularization of the Boussinesq systemis performed in frequency space using Fourier theory. Existence and uniqueness of weak solutions with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray-Hopf solution of the Boussinesq system are established as the regularizing parameter α vanishes. The proofs are done in the frequency space and use energy methods, the Arselà-Ascoli compactness theorem and a Friedrichs-like approximation scheme.

scholarly journals On the well-posedness and large-time behavior of higher order Boussinesq system

Nonlinearity ◽  
2019 ◽  
Vol 32 (5) ◽  
pp. 1852-1881 ◽  
Author(s):  
Roberto A Capistrano-Filho ◽  
Fernando A Gallego ◽  
Ademir F Pazoto
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Higher Order ◽  
Boussinesq System ◽  
Well Posedness ◽  
Time Behavior

scholarly journals On the local well-posedness of a Benjamin-Ono-Boussinesq system

2005 ◽  
Vol 2005 (22) ◽  
pp. 3609-3630
Author(s):  
Ruying Xue
Keyword(s):  
Sobolev Space ◽  
Boussinesq System ◽  
Well Posedness ◽  
Well Posed

Consider a Benjamin-Ono-Boussinesq systemηt+ux+auxxx+(uη)x=0,ut+ηx+uux+cηxxx−duxxt=0, wherea,c, anddare constants satisfyinga=c>0,d>0ora<0,c<0,d>0. We prove that this system is locally well posed in Sobolev spaceHs(ℝ)×Hs+1(ℝ), withs>1/4.

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