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)

Mohammad Ghani

doi:10.1016/j.nonrwa.2021.103355

Local well-posedness of Boussinesq equations for MHD convection with fractional thermal diffusion in sobolev space H^s(Rⁿ)×H^s+1−ϵ(Rⁿ)×H^s+α−ϵ(Rⁿ)

Mohammad Ghani

Faculty of Advanced Technology and Multidiscipline

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	103355
Journal	Nonlinear Analysis: Real World Applications
Volume	62
DOIs	https://doi.org/10.1016/j.nonrwa.2021.103355
Publication status	Published - Dec 2021

Keywords

Boussinesq-MHD
Fractional thermal diffusion
Local well-posedness
Sobolev space

Access to Document

10.1016/j.nonrwa.2021.103355

Cite this

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title = "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)",

abstract = "In this paper, we study the local well-posedness of the Boussinesq equation for MHD convection with fractional thermal diffusion in Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn) with [Formula presented] and any small enough ϵ>0 such that [Formula presented] and [Formula presented]. We present here the fractional operator (−Δ)αθ for α>1 which is estimated by using Littlewood–Paley projection.",

keywords = "Boussinesq-MHD, Fractional thermal diffusion, Local well-posedness, Sobolev space",

author = "Mohammad Ghani",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2021",

month = dec,

doi = "10.1016/j.nonrwa.2021.103355",

language = "English",

volume = "62",

journal = "Nonlinear Analysis: Real World Applications",

issn = "1468-1218",

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T1 - 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)

AU - Ghani, Mohammad

PY - 2021/12

Y1 - 2021/12

N2 - In this paper, we study the local well-posedness of the Boussinesq equation for MHD convection with fractional thermal diffusion in Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn) with [Formula presented] and any small enough ϵ>0 such that [Formula presented] and [Formula presented]. We present here the fractional operator (−Δ)αθ for α>1 which is estimated by using Littlewood–Paley projection.

AB - In this paper, we study the local well-posedness of the Boussinesq equation for MHD convection with fractional thermal diffusion in Hs(Rn)×Hs+1−ϵ(Rn)×Hs+α−ϵ(Rn) with [Formula presented] and any small enough ϵ>0 such that [Formula presented] and [Formula presented]. We present here the fractional operator (−Δ)αθ for α>1 which is estimated by using Littlewood–Paley projection.

KW - Boussinesq-MHD

KW - Fractional thermal diffusion

KW - Local well-posedness

KW - Sobolev space

UR - http://www.scopus.com/inward/record.url?scp=85106549230&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2021.103355

DO - 10.1016/j.nonrwa.2021.103355

M3 - Article

AN - SCOPUS:85106549230

SN - 1468-1218

VL - 62

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

M1 - 103355