Lagrangian regularity of the electron magnetohydrodynamics flow on a bounded domain

In this paper we investigate the regularity in time of Lagrangian flow associated with electron magnetohydrodynamics (e-MHD) equations on a bounded domain smooth (ultradifferentiable) boundary. This model is widely used controlled magnetic fusion, space and astrophysics plasmas also physics solids. We show that initial data limited smoothness Sobolev spaces induce flow-map X vector potential A (viz. evaluated at spatial point X), which are ultradifferentiable time, two particular cases real analytic Gevrey regularity. It turns out canonical momentum P, field B, electric E inherit property. Among others, proof makes crucial use novel formulation e-MHD terms fields (X,A,P,B,E). by-product constructive design arbitrary high-order semi-Lagrangian schemes to solve domain.