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arXiv · 2603.24611

The Spatial Hydrodynamic Attractor: Resurgence of the Gradient Expansion

Mahdi Kooshkbaghi
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Abstract

Far-from-equilibrium kinetic systems collapse onto a hydrodynamic attractor, traditionally approximated by a gradient expansion. While temporal gradient series are non-Borel summable and require transseries completions, the analytic structure of the spatial expansion has remained elusive. Here, we derive exact closed-form Chapman--Enskog coefficients at all orders via Lagrange inversion and prove that the non-relativistic spatial gradient series, though factorially divergent, is strictly Borel summable. Furthermore, we show that this divergence originates from unbounded Galilean velocities; enforcing relativistic causality yields a convergent spatial hydrodynamic expansion with finite radius. Together with prior temporal results, our findings suggest that the hydrodynamic gradient expansion is always Borel summable, pointing to a non-perturbative route from kinetic theory to hydrodynamics.

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Mahdi Kooshkbaghi. 2026-03-23. The Spatial Hydrodynamic Attractor: Resurgence of the Gradient Expansion. https://arxiv.org/abs/2603.24611

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