Incompressible limit for the free surface Navier-Stokes system

Nader Masmoudi, Frédéric Rousset, Changzhen Sun

Research output: Contribution to journalArticlepeer-review


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 ε, ε 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.

Original languageEnglish (US)
Article number9
JournalAnnals of PDE
Issue number1
StatePublished - Jun 2023


  • 35B34
  • 35B35
  • 35B65
  • Boundary layer
  • Free surface viscous fluids
  • Low Mach number limit
  • Uniform regularity

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology
  • Applied Mathematics


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