Existence and regularity of solution for a model in magnetohydrodynamics. (January 2020)

• Record Type: Journal Article
• Authors: Amrouche, Chérif; Boukassa, Saliha
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: Magnetohydrodynamics -- Stokes equations -- Navier–stokes equations -- Vector potentials -- Weak solutions -- Strong solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111602
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study a model of magnetohydrodynamics problem and prove the existence of weak solution to the stationary magnethohydrodynamic system in a three dimensional bounded domain Ω of class C 1, 1 . To our knowledge, all previous works consider the domain Ω simply-connected. Our proof is based on some weak estimates concerning vectors potential in negative Sobolev spaces. We also give some regularity results in L p -theory.