Pré-Publication, Document De Travail Année : 2021

Incompressible limit for the free surface Navier-Stokes system

Résumé

We establish uniform regularity estimates with respect to the Mach number for the three-dimensional free surface compressible Navier-Stokes system in the case of slightly well-prepared initial data in the sense that the acoustic components like the divergence of the velocity field are of size $\sqrt{\varepsilon}$, $\varepsilon$ being the Mach number. These estimates allow us to justify the convergence towards the free surface incompressible Navier-Stokes system in the low Mach number limit. One of the main difficulties is the control of the regularity of the surface in presence of boundary layers with fast oscillations.

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Dates et versions

hal-03385798 , version 1 (19-10-2021)

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Nader Masmoudi, Frédéric Rousset, Changzhen Sun. Incompressible limit for the free surface Navier-Stokes system. 2021. ⟨hal-03385798⟩
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