Abstract
The Hamiltonian structure is given for ideal relativistic multifluid plasma dynamics in the laboratory frame with the Hamiltonian functional equaling the relativistic energy minus the mass energy. The noncanonical Poisson bracket for this system turns out to be the same as for the nonrelativistic multifluid plasma, but with dynamical variables replaced by their relativistic counterparts. New constants of the motion are then derived from the Hamiltonian structure and used as Lyapunov functionals for proving sufficient conditions for nonlinear stability of relativistic multifluid plasma equilibria. The nonrelativistic limit of the formulation is uniformly regular, and nonlinear Lyapunov stability conditions derived previously for a nonrelativistic multifluid plasma reemerge in that limit.
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