2021 # Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field with vertical dissipation

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“…One may refer to [1,2,3,12,13,15,16,17,18,31,34] and the references therein. For the BMHD system, the known result to us is the nonlinear stability of the Couette flow for the 2D BMHD equations with only vertical disspation in a uniform magnetic field, established by the first two authors and Dai [5], which used the method of Deng, Wu and Zhang [10]. This result inspires us to study whether the 2D BMHD equations with mixed partial dissipation remain stable for some other kinds of equilibriums, say, the hydrostatic equilibrium.…”

confidence: 89%

“…One may refer to [1,2,3,12,13,15,16,17,18,31,34] and the references therein. For the BMHD system, the known result to us is the nonlinear stability of the Couette flow for the 2D BMHD equations with only vertical disspation in a uniform magnetic field, established by the first two authors and Dai [5], which used the method of Deng, Wu and Zhang [10]. This result inspires us to study whether the 2D BMHD equations with mixed partial dissipation remain stable for some other kinds of equilibriums, say, the hydrostatic equilibrium.…”

confidence: 89%

“…Recently, important progress has been made on the global stability for Boussinesq-MHD system; see other works [4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. And Bian et al 17 have proved the nonlinear stability of Couette flow in a uniform magnetic field for this system with only vertical dissipation, in which some ideas are shared from the paper of Deng et al 18 for 2D Boussinesq system with vertical dissipation. It is noted that Dong et al 19 have established the nonlinear stability of hydrostatic equilibrium (u he = 0, p he = 1 2 𝑦 2 , 𝜃 he = 𝑦) for the system (1.1) with magnetic field B = 0.…”

confidence: 96%