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Initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection

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  • This paper is concerned with the initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection. We show that the system has a unique classical solution for $H^3$ initial data, and the non-slip boundary condition for velocity field and the perfectly conducting wall condition for magnetic field. In addition, we show that the kinetic energy is uniformly bounded in time.
    Mathematics Subject Classification: Primary: 35Q35, 76D03.


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