This analysis demonstrates time-asymptotic nonlinear stability in first-order relativistic viscous hydrodynamics, highlighting significant improvements over earlier findings on Fourier modes.
The paper shows time-asymptotic nonlinear stability of homogenous reference states for a very general class of first-order descriptions of relativistic viscous hydrodynamics. This result, sharper than the previously known mere decay of individual Fourier modes, thus applies to the descriptions formulated in Freistühler and Temple [Proc. R. Soc. London, Ser. A 470, 20140055 (2014) and J. Math. Phys. 59, 063101 (2018)], Bemfica, Disconzi, and Noronha [Phys. Rev. D 98, 104064 (2018) and Phys. Rev. D 100, 104020 (2019)], and Freistühler [J. Math. Phys. 61, 033101 (2020)].
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Freistühler et al. (2025) studied this question.
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