Lyapunov stability of relativistic fluids and plasmas

Lyapunov stability of relativistic ideal fluid and plasma equilibria is studied analytically using the energy-Casimir method. Two- and three-dimensional relativistic equilibria in a fixed bounded domain are investigated within the framework of the macroscopic multifluid plasma model. Linearized Lyapunov stability conditions and stability norms are given, accounting for warm-plasma effects as well as relativistic and electromagnetic effects. The resulting Lyapunov stability conditions are compared to spectral stability analyses for relativistic cold plasmas in various examples and special cases, including (1) non-neutral electron flow in a planar diode and (2) circularly symmetric plasma flow enclosed in a coaxial waveguide. These linearized stability results can be extended readily to nonlinear Lyapunov stability conditions for finite-amplitude perturbations by employing standard convexity arguments for the Lyapunov functions given here. The relativistic stability conditions are shown to reduce either to their nonrelativistic counterparts or to trivial identities in the nonrelativistic limit.