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To further confirm the causality and stability of a second-order hyperbolicsystem of partial differential equations that models the relativistic dynamicsof barotropic fluids with viscosity and heat conduction (H. Freist\"uhler andB. Temple, J. Math. Phys. 59 (2018)), this paper studies the Fourier-Laplacemodes of this system and shows that all such modes, relative to arbitraryLorentz frames, (a) decay with increasing time and (b) travel at subluminalspeeds. Stability is also shown for the related model of non-barotropic fluids(H. Freist\"uhler and B. Temple. Proc. R. Soc. A 470 (2014) and Proc. R. Soc. A473 (2017)). Even though these properties had been known for a while in thesense of numerical evidence, the fully analytical proofs for the subluminalityof modes of arbitrary wave numbers in arbitrary frames given here appear to bethe first regarding any five-field formulation of dissipative relativisticfluid dynamics.

Decay and Subluminality of Modes of all Wave Numbers in the Relativistic Dynamics of Viscous and Heat Conductive Fluids