Decay properties of axially symmetric D-solutions to the steady incompressible magnetohydrodynamic equations. (October 2022)

• Record Type: Journal Article
• Authors: Weng, Shangkun; Zhou, Yan
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: primary 35Q35 -- secondary 76W05; Magnetohydrodynamics equations -- Decay rate -- Axially symmetric -- Scaling argument -- Weighted energy estimates; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103599
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate the decay properties of axially symmetric solutions to the steady incompressible magnetohydrodynamic equations in R 3 with finite Dirichlet integral. We first derive the decay rates of general D-solutions to the axisymmetric MHD equations. In the special case where the magnetic field only has the swirl component h ( r, z ) = h θ ( r, z ) e θ, we obtain better decay rates. The last result examines the decay rates along the axis O z also within the special class of D-solutions with only swirl magnetic field. The main tool in this paper is the combination of the scaling argument, the Brezis–Gallouet inequality and the weighted energy estimate.