High viscosity limit for the multi-dimensional compressible Navier-Stokes equations

Raphaël Danchin

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arXiv · 2603.15209

High viscosity limit for the multi-dimensional compressible Navier-Stokes equations

Raphaël Danchin

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Abstract

We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant viscosity coefficients, we establish that, after diffusive rescaling, the density tends to satisfy a transport equation with nonlinear damping which is globally well-posed, even for large data. Similar results are proved for variable viscosity coefficients. In this latter case, the damping term in the limit equation of the density is nonlocal.

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Raphaël Danchin. 2026-03-16. High viscosity limit for the multi-dimensional compressible Navier-Stokes equations. https://arxiv.org/abs/2603.15209

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