Incompressible limit for the free surface Navier-Stokes system

Nader Masmoudi; Frédéric Rousset; Changzhen Sun

doi:10.1007/s40818-023-00148-7

Incompressible limit for the free surface Navier-Stokes system

Nader Masmoudi, Frédéric Rousset, Changzhen Sun

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Article number	9
Journal	Annals of PDE
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s40818-023-00148-7
State	Published - Jun 2023

Keywords

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

ASJC Scopus subject areas

Analysis
Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology
Applied Mathematics

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10.1007/s40818-023-00148-7

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title = "Incompressible limit for the free surface Navier-Stokes system",

abstract = "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.",

keywords = "35B34, 35B35, 35B65, Boundary layer, Free surface viscous fluids, Low Mach number limit, Uniform regularity",

author = "Nader Masmoudi and Fr{\'e}d{\'e}ric Rousset and Changzhen Sun",

note = "Funding Information: The work of N. Masmoudi is supported by NSF grant DMS-1716466 and by Tamkeen under the NYU Abu Dhabi Research Institute grant of the center SITE. F. Rousset was partially supported by the ANR projects ANR-18-CE40-0027 and ANR-18-CE40-0020-01. C. Sun benefits the postdoc fellowship funded by Labex CIMI. This work was conducted during the PhD study of the third author in LMO, he would like to thank the institute for providing great research environment. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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AU - Masmoudi, Nader

AU - Rousset, Frédéric

AU - Sun, Changzhen

N1 - Funding Information: The work of N. Masmoudi is supported by NSF grant DMS-1716466 and by Tamkeen under the NYU Abu Dhabi Research Institute grant of the center SITE. F. Rousset was partially supported by the ANR projects ANR-18-CE40-0027 and ANR-18-CE40-0020-01. C. Sun benefits the postdoc fellowship funded by Labex CIMI. This work was conducted during the PhD study of the third author in LMO, he would like to thank the institute for providing great research environment. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2023/6

Y1 - 2023/6

N2 - 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.

AB - 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.

KW - 35B34

KW - 35B35

KW - 35B65

KW - Boundary layer

KW - Free surface viscous fluids

KW - Low Mach number limit

KW - Uniform regularity

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Incompressible limit for the free surface Navier-Stokes system

Abstract

Keywords

ASJC Scopus subject areas

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