Local well-posedness of Boussinesq equations for MHD convection with fractional thermal diffusion in sobolev space <mml:...

What is it about?

In this paper, we study the local well-posedness of the Boussinesq equation for MHD convection with fractional thermal diffusion in H s (R n)× H s+ 1− ϵ (R n)× H s+ α− ϵ (R n) with s> n 2− 1 and any small enough ϵ> 0 such that s+ 1− ϵ> n 2 and s+ α− ϵ≥ s+ 2−(ϵ+ α)> n 2. We present here the fractional operator (− Δ) α θ for α> 1 which is estimated by using Littlewood–Paley projection.

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