Local well-posedness of Boussinesq equations for MHD convection with fractional thermal diffusion in sobolev space Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn). (December 2021) - Ghani, Mohammad
Abstract: 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.