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)

• Record Type: Journal Article
• Authors: Ghani, Mohammad
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Boussinesq-MHD -- Sobolev space -- Local well-posedness -- Fractional thermal diffusion; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103355
• Languages: English
• ISSNs: 1468-1218

Abstract

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.