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This paper is concerned with the Cauchy problem of the two‐dimensional Euler–Boussinesq system with stratification effects. We obtain the global existence of a unique solution to this system without assumptions of small initial data in Sobolev spaces. Copyright © 2017 John Wiley & Sons, Ltd.
In this paper, we establish the nonlinear stability and large time behavior of hydrostatic equilibrium in a uniform magnetic field for the 2D Boussinesq system with magnetohydrodynamics convection on spatial domain normalΩ=𝕋×ℝ with partial dissipation. This is the important part of further work about the stability/instability of shear flow which is the combination of hydrostatic equilibrium and Couette/shear flow in a uniform magnetic field with partial dissipation.
In this paper, we investigate the global existence and uniqueness of strong solutions to the two‐dimensional Boussinesq‐MHD equations without the temperature diffusion for general initial data in with . As an application, we shall prove the propagation of the regularity of the interface between fluids with different temperatures.
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