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Low Mach Number Limit of Viscous Polytropic Flows: Formal Asymptotics in the Periodic Case
Author(s) -
Bresch D.,
Desjardins B.,
Grenier E.,
Lin C.K.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01440
Subject(s) - polytropic process , mach number , limit (mathematics) , mathematical analysis , boundary value problem , mathematics , nonlinear system , compressibility , compressible flow , physics , classical mechanics , mechanics , quantum mechanics
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.