Mild Ill-posedness for the 2D MHD-Boussinesq System with a Background Magnetic Field

Abstract

In this paper, we study the mild ill-posedness problem of the two-dimensional MHD-Boussinesq system with the temperature-dependent thermal diffusivity and electrical conductivity near the background magnetic field in L^∞. Here we construct a sequence of initial data so that the L^∞-norm of vorticity of the corresponding solution is mildly ill-posed.

Keywords

2D MHD-Boussinesq system / ill-posedness / background magnetic field

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