Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case

D. Bresch; B. Desjardins; E. Grenier; C. K. Lin

doi:10.1111/1467-9590.01440

Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case

D. Bresch^*
, B. Desjardins
, E. Grenier
, C. K. Lin

^*Corresponding author for this work

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

73 Citations (Scopus)

Abstract

This article is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for polytropic fluids with periodic boundary conditions and ill-prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.

Original language	English
Pages (from-to)	125-149
Number of pages	25
Journal	Studies in Applied Mathematics
Volume	109
Issue number	2
DOIs	https://doi.org/10.1111/1467-9590.01440
Publication status	Published - Aug 2002
Externally published	Yes

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title = "Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case",

abstract = "This article is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for polytropic fluids with periodic boundary conditions and ill-prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.",

author = "D. Bresch and B. Desjardins and E. Grenier and Lin, \{C. K.\}",

year = "2002",

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AU - Bresch, D.

AU - Desjardins, B.

AU - Grenier, E.

AU - Lin, C. K.

PY - 2002/8

Y1 - 2002/8

N2 - This article is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for polytropic fluids with periodic boundary conditions and ill-prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.

AB - This article is devoted to the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for polytropic fluids with periodic boundary conditions and ill-prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.

UR - https://www.scopus.com/pages/publications/0036702720

U2 - 10.1111/1467-9590.01440

DO - 10.1111/1467-9590.01440

M3 - Article

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VL - 109

SP - 125

EP - 149

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

IS - 2

ER -

Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case

Abstract

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