Stability threshold for 2D shear flows of the Boussinesq system near Couette

In this paper, we consider the nonlinear stability for the shear flows of the Boussinesq system in a domain T×R. We prove the nonlinear stability of the shear flow (US,ΘS)=((eνt∂yyU(y),0)⊤,αy) with U(y) close to y and α ≥ 0 in Sobolev spaces for the following two cases: (i) α ≥ 0 is small scaling wi...

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Published in:Journal of mathematical physics 2022-08, Vol.63 (8)
Main Authors: Bian, Dongfen, Pu, Xueke
Format: Article
Language:English
Subjects:
Boussinesq equations
Diffusion coefficient
Flow stability
Perturbation
Physics
Shear flow
Sobolev space
Two dimensional flow
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description In this paper, we consider the nonlinear stability for the shear flows of the Boussinesq system in a domain T×R. We prove the nonlinear stability of the shear flow (US,ΘS)=((eνt∂yyU(y),0)⊤,αy) with U(y) close to y and α ≥ 0 in Sobolev spaces for the following two cases: (i) α ≥ 0 is small scaling with the viscosity coefficients and initial perturbation ≲min{ν,μ}1/2 and (ii) α > 0 is not small, the heat diffusion coefficient μ is fixed, and initial perturbation ≲ν1/2.
doi_str_mv 10.1063/5.0091052
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source American Institute of Physics (AIP) Publications; American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list)
subjects Boussinesq equations
Diffusion coefficient
Flow stability
Perturbation
Physics
Shear flow
Sobolev space
Two dimensional flow
title Stability threshold for 2D shear flows of the Boussinesq system near Couette
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