Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

Liu, Huimin; Bian, Dongfen; Pu, Xueke

doi:10.1007/s00033-019-1126-y

Cited by 28 publications

(12 citation statements)

References 29 publications

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“…An anisotropic viscous version of the BFeD system was studied in [6]. Eventually, a relatively closed (from the mathematical point of view) MHD model was investigated in [40] and a its Boussinesq-MHD version (without diffusion) in [26]. Let us mention that in the latter reference, the uniqueness was obtained only for regular solutions, and our argument in the present contribution combined with ideas from [40] can improve the result.…”

Section: The Physical Modelmentioning

confidence: 79%

Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media

Titi¹,

Trabelsi²

2022

Preprint

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We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bénard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in L 2 and H 1 . Eventually, we comment on the applicability of a data assimilation algorithm to our system.

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Section: The Physical Modelmentioning

confidence: 79%

Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media

Titi¹,

Trabelsi²

2022

Preprint

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“…Two fundamental problems, the global regularity problem and the stability problem, have been among the main driving forces in advancing the mathematical theory on the Boussinesq-MHD system. Significant progress has been made on the global regularity of the nonlinear Boussinesq-MHD system [7,8,9,10,23,24,26,37,38]. The goal of this paper is the nonlinear stability around the Couette flow (u sh = (y, 0), b sh = (1, 0), p sh = 0, θ sh = 0).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field

Bian,

Dai,

Mao

2020

Preprint

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In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain T × R and establishes the nonlinear stability of the Couette flow (u sh = (y, 0), b sh = (1, 0), p sh = 0, θ sh = 0). The novelty in this paper is that we design a new Fourier multiplier operator by using the properties of the enhanced dissipation to overcome the difficult term ∂ xy (−∆) −1 j in the linearized and nonlinear system. Then, we prove the asymptotic stability for the linearized system. Finally, we establish the nonlinear stability for the full system by bootstrap principle.

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“…In the 3D case, Larios-Pei [27] proved the the local well-posedness results in Sobolev space. Liu-Bian-Pu [20] proved the global well-posedness of strong solutions with nonlinear damping term in the momentum equations. Regarding the MHD-Bénard system, some progress has also been made in 2D and 3D case.…”

Section: Introductionmentioning

confidence: 98%