Low Mach number limit of the compressible Navier-Stokes system for large initial date with critical regularity on the torus

Sai Li

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arXiv · 2603.00894

Low Mach number limit of the compressible Navier-Stokes system for large initial date with critical regularity on the torus

Sai Li

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Abstract

We study the low Mach number limit of the compressible Navier-Stokes equations on the torus. For large initial data with critical regularity, we prove that solutions to the compressible Navier-Stokes system exist as long as the corresponding solutions to the incompressible Navier-Stokes system exist, provided that the Mach number is sufficiently small. Furthermore, we establish the convergence of solutions of the compressible system to those of the incompressible system as the Mach number tends to zero. Our approach combines high-medium-low frequency analysis of density and velocity with the solution filtering technique via acoustic wave groups. This work provides an affirmative answer to the problem posed by Danchin [Amer.J.Math.,124(2002),1153-1219]:"Does convergence hold for large data with critical regularity?"

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Sai Li. 2026-03-01. Low Mach number limit of the compressible Navier-Stokes system for large initial date with critical regularity on the torus. https://arxiv.org/abs/2603.00894

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