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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  1. Arrieta, J.M., Krejčiřík, D., Geometric versus spectral convergence for the Neumann Laplacian under exterior perturbation of the domain, Integral Methods in Sciences and Engineering 1 (2010), 9–19. (2010) MR2663114
  2. Bucur, D., Feireisl, E., Nečasová, Š., Wolf, J., 10.1016/j.jde.2008.02.040, J. Differential Equations 244 (2008), 2890–2908. (2008) MR2418180DOI10.1016/j.jde.2008.02.040
  3. Feireisl, E., 10.1007/s00220-009-0954-6, Commun. Math. Phys. 294 (2010), 73–95. (2010) MR2575476DOI10.1007/s00220-009-0954-6
  4. Feireisl, E., 10.1080/03605302.2011.602168, Commun. Partial Differential Equations 36 (2011), 1778–1796. (2011) MR2832163DOI10.1080/03605302.2011.602168
  5. Feireisl, E., Karper, T., Kreml, O., Stebel, J., 10.1142/S0218202513500371, Math. Models Methods Appl. Sci. 23 (13) (2013), 2465–2493. (2013) MR3109436DOI10.1142/S0218202513500371
  6. Feireisl, E., Novotný, A., Singular limits in thermodynamics of viscous fluids, Birkhäuser, Basel, 2009. (2009) MR2499296
  7. Feireisl, E., Schonbek, M., On the Oberbeck-Boussinesq approximation on unbounded domains, Nonlinear partial differential equations, Abel Symposial (Holden, H., Karlsen, K.H., eds.), vol. 7, Springer, Berlin, 2012. (2012) MR3289362
  8. Jones, P.W., 10.1007/BF02392869, Acta Math. 147 (1981), 71–88. (1981) DOI10.1007/BF02392869
  9. Klein, R., Botta, N., Schneider, T., Munz, C.D., Roller, S., Meister, A., Hoffmann, L., Sonar, T., 10.1023/A:1004844002437, J. Engrg. Math. 39 (2001), 261–343. (2001) MR1826065DOI10.1023/A:1004844002437
  10. Lighthill, J., Waves in Fluids, Cambridge University Press, 1978. (1978) 
  11. Wróblewska-Kamińska, A., 10.1137/15M1029655, SIAM J. Math. Anal. 49 (5) (2017), 3299–3334. (2017) MR3697164DOI10.1137/15M1029655
  12. Zeytounian, R.K., 10.1016/S1631-0721(03)00120-7, C.R. Mecanique 331 (2003), 575–586. (2003) DOI10.1016/S1631-0721(03)00120-7
  13. Zeytounian, R.K., Theory and Applications of Viscous Fluid Flows, Springer, Berlin, 2004. (2004) MR2028446

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