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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Bibliographic Details
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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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0091052