Decay properties of axially symmetric D-solutions to the steady incompressible magnetohydrodynamic equations. (October 2022) - Weng, Shangkun; Zhou, Yan
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.