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arXiv · 2601.19846

Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations

Qian Huang·Christian Rohde·Ruixi Zhang
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Abstract

We investigate a two-parameter hyperbolic relaxation approximation to the incompressible Navier-Stokes equations, incorporating a first-order relaxation and the artificial compressibility method. With vanishingly small perturbations of initial velocity, we rigorously prove the simultaneous convergence of fluid velocity and pressure toward the Navier-Stokes limit in the three-dimensional case by constructing an intermediate affine system to obtain the necessary error estimates for the pressure. Furthermore, we extend the velocity convergence analysis to the case of $\mathcal O(1)$ initial velocity perturbations, and establish the global-in-time recovery of the velocity field using a modulated energy structure and delicate bootstrap arguments in both two- and three-dimensional settings.

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Qian Huang, Christian Rohde, Ruixi Zhang. 2026-01-27. Convergence of a two-parameter hyperbolic relaxation system toward the incompressible Navier-Stokes equations. https://arxiv.org/abs/2601.19846

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