Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

Aneta Wróblewska-Kamińska

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 2, page 231-243
  • ISSN: 0044-8753

Abstract

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We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter ε → 0 , the Froude number proportional to ε and when the fluid occupies large domain with spatial obstacle of rough surface varying when ε → 0 . The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.

How to cite

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Wróblewska-Kamińska, Aneta. "Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid." Archivum Mathematicum 059.2 (2023): 231-243. <http://eudml.org/doc/298985>.

@article{Wróblewska2023,
abstract = {We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\varepsilon \rightarrow 0$, the Froude number proportional to $\sqrt\{\varepsilon \}$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\varepsilon \rightarrow 0$. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.},
author = {Wróblewska-Kamińska, Aneta},
journal = {Archivum Mathematicum},
keywords = {Oberbeck-Boussinesq approximation; singular limit; low Mach number; unbounded domain; compressible Navier-Stokes-Fourier system; weak solutions; no-slip boundary condition},
language = {eng},
number = {2},
pages = {231-243},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid},
url = {http://eudml.org/doc/298985},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Wróblewska-Kamińska, Aneta
TI - Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 2
SP - 231
EP - 243
AB - We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\varepsilon \rightarrow 0$, the Froude number proportional to $\sqrt{\varepsilon }$ and when the fluid occupies large domain with spatial obstacle of rough surface varying when $\varepsilon \rightarrow 0$. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.
LA - eng
KW - Oberbeck-Boussinesq approximation; singular limit; low Mach number; unbounded domain; compressible Navier-Stokes-Fourier system; weak solutions; no-slip boundary condition
UR - http://eudml.org/doc/298985
ER -

References

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