We obtain a formal integral solution to the $3+1\mathrm{D}$ Boltzmann equation in relaxation-time approximation. The gradient series obtained from this integral solution contains exponentially decaying nonhydrodynamic terms. It is shown that this gradient expansion can have a finite radius of convergence under certain assumptions of analyticity. We then argue that, in the relaxation-time model, proximity to local thermal equilibrium is not necessary for the system to be described by hydrodynamic equations.

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• Quark-gluon plasma
• Relativistic kinetic theory
• Hydrodynamic models
• Relativistic heavy-ion collisions
• Relativistic hydrodynamics