Linearization principle for a toroidal Hall current plasma with viscosity and resistivity

Abstract

In this paper the stability analysis of an incompressible toroidal Hall Current plasma with resistivity and viscosity on the basis of the linearization of the governing equations and boundary condition is rigorously justified. A nonlinear local existence theorem for an initial-boundary value problem is first proved, and local stable and unstable invariant manifolds of a nonlinear resolving operator are then constructed. It is shown that linear stability implies nonlinear stability and global existence, and linear instability implies nonlinear instability in some sense.