Scale invariant solutions in relativistic hydrodynamics

@misc{calzetta2026scale,
  title = {{Scale invariant solutions in relativistic hydrodynamics}},
  author = {Esteban Calzetta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.25329},
  eprint = {2605.25329},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.25329},
}

TY  - UNPB
TI  - Scale invariant solutions in relativistic hydrodynamics
AU  - Esteban Calzetta
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2605.25329
UR  - https://arxiv.org/abs/2605.25329
AB  - The goal of this work is to describe the scale invariant solutions of a typical relativistic hydrodynamic model. We shall take as representative model an Israel-Stewart framework, where the energy-momentum conservation laws for a conformal invariant fluid are supplemented by a Cattaneo-Maxwell equation for its viscous energy-momentum tensor. In these models the viscous energy-momentum tensor relaxes to its Landau-Lifshitz value on a finite time scale. We assume the parameters of the model depend on the speed of light c in such a way that as c→∞ the fluid becomes an incompressible fluid obeying the Navier-Stokes equations. We seek the scale invariant solutions for this model and find that for finite c there are two basic patterns, one which reproduces Kolmogorov turbulence when c→∞, and another whose damping rate diverges in that limit. We point out the scaling relations that allow the latter flow pattern to sustain an entropy cascade.
ER  -