Asymptotic Shallow Models Arising in Magnetohydrodynamics

Abstract In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, present magnetic analogue 2D Green–Naghdi water waves under a weak pressure assumption presence weakly sheared vorticity and currents. Our method is inspired ideas hydrodynamic developed Castro Lannes (2014) to reduce three-dimensional dynamics current finite cascade two dimensional can be closed at precision model.