[Un système multi-fluide compressible avec de nouveaux termes de relaxation physiques]
Dans cet article, nous étudions la propagation d'oscillations de densité dans les solutions des équations de Navier-Stokes compressibles fluides à viscosité variable. Nous appliquons cette analyse à la dérivation rigoureuse d'un système de type Baer-Nunziatio pour les écoulements multi-fluide. Le modèle obtenu inclut de nouveaux termes de relaxation dans les équations sur les fractions volumiques des composants du mélange. Ces termes résultent des différences entre les lois de viscosité et de pression dans les différents composants.
In this paper, we study the propagation of density-oscillations in solutions to density-dependent compressible Navier Stokes system. As a consequence to this analysis, we derive rigorously a generalization of the one-velocity Baer-Nunziato model for multifluid flows. The derived model includes a new relaxation term, in the PDE that governs the volume fraction of the component fluids, that encodes the change of viscosity and pressure between them.
Keywords: Compressible Navier-Stokes, density-dependent viscosity, multifluid flows, Baer-Nunziato, homogenization, Young measures, effective flux, relaxation terms.
Mot clés : Navier-Stokes compressible, viscosité variable, systèmes multi-fluides, Baer-Nunziato, homogénéisation, mesures de Young, flux effectif, termes de relaxation.
@article{ASENS_2019__52_1_257_0,
author = {Bresch, Didier and Hillairet, Matthieu},
title = {A {Compressible} {Multifluid} {System} with {New} {Physical} {Relaxation} {Terms}},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {255--295},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 52},
number = {1},
year = {2019},
doi = {10.24033/asens.2387},
zbl = {1421.35241},
language = {en},
url = {http://archive.numdam.org/articles/10.24033/asens.2387/}
}
TY - JOUR AU - Bresch, Didier AU - Hillairet, Matthieu TI - A Compressible Multifluid System with New Physical Relaxation Terms JO - Annales scientifiques de l'École Normale Supérieure PY - 2019 SP - 255 EP - 295 VL - 52 IS - 1 PB - Société Mathématique de France. Tous droits réservés UR - http://archive.numdam.org/articles/10.24033/asens.2387/ DO - 10.24033/asens.2387 LA - en ID - ASENS_2019__52_1_257_0 ER -
%0 Journal Article %A Bresch, Didier %A Hillairet, Matthieu %T A Compressible Multifluid System with New Physical Relaxation Terms %J Annales scientifiques de l'École Normale Supérieure %D 2019 %P 255-295 %V 52 %N 1 %I Société Mathématique de France. Tous droits réservés %U http://archive.numdam.org/articles/10.24033/asens.2387/ %R 10.24033/asens.2387 %G en %F ASENS_2019__52_1_257_0
Bresch, Didier; Hillairet, Matthieu. A Compressible Multifluid System with New Physical Relaxation Terms. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 1, pp. 255-295. doi : 10.24033/asens.2387. http://archive.numdam.org/articles/10.24033/asens.2387/
On the error of quasi-averaging of the equations of motion of a viscous barotropic medium with rapidly oscillating data, Comp. Maths. Math. Phys., Volume 36 (1996), pp. 1415-1428 | Zbl
Sur la théorie globale des équations de Navier-Stokes compressibles, Actes des 33es journées Équations aux dérivées partielles, Evian (2006)
A multi-fluid compressible system as the limit of weak solutions of the isentropic compressible Navier-Stokes equations, Arch. Ration. Mech. Anal., Volume 201 (2011), pp. 647-680 (ISSN: 0003-9527) | DOI | MR | Zbl
Note on the derivation of multi-component flow systems, Proc. Amer. Math. Soc., Volume 143 (2015), pp. 3429-3443 (ISSN: 0002-9939) | DOI | MR | Zbl
, Applied Mathematical Sciences, 135, Springer, 1999, 308 pages (ISBN: 0-387-98380-5) | DOI | MR | Zbl
On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., Volume 3 (2001), pp. 358-392 (ISSN: 1422-6928) | DOI | MR | Zbl
Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D, Math. Nachr., Volume 291 (2018), pp. 2188-2203 (ISSN: 0025-584X) | DOI | MR | Zbl
Propagation of density-oscillations in solutions to the barotropic compressible Navier-Stokes system, J. Math. Fluid Mech., Volume 9 (2007), pp. 343-376 (ISSN: 1422-6928) | DOI | MR | Zbl
, Springer, 2006, 462 pages (ISBN: 978-0-387-28321-0; 0-387-28321-8) | DOI | MR | Zbl
A model system of equations for the one-dimensional motion of a gas, J. Diff. Eq., Volume 4 (1968), pp. 374-380 (ISSN: 0374-0641) | MR | Zbl
, Oxford Lecture Series in Mathematics and its Applications, The Clarendon Press Univ. Press, 1998, 237 pages (ISBN: 0-19-851487-5) | MR | Zbl
Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations, SIAM J. Math. Anal., Volume 39 (2007/08), pp. 1344-1365 (ISSN: 0036-1410) | DOI | MR | Zbl
, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series), 73, Birkhäuser, 2012, 457 pages (ISBN: 978-3-0348-0366-3) | DOI | MR | Zbl
Asymptotics of homogeneous oscillations in a compressible viscous fluid, Bol. Soc. Brasil. Mat. (N.S.), Volume 32 (2001), pp. 435-442 (ISSN: 0100-3569) | DOI | MR | Zbl
Variations de grande amplitude pour la densité d'un fluide visqueux compressible, Phys. D, Volume 48 (1991), pp. 113-128 (ISSN: 0167-2789) | DOI | MR | Zbl
, Systems of nonlinear partial differential equations (Oxford, 1982) (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.), Volume 111, Reidel, 1983, pp. 263-285 | DOI | MR | Zbl
Propagation of oscillations in the solutions of 1-D compressible fluid equations, Comm. Partial Differential Equations, Volume 17 (1992), pp. 347-370 (ISSN: 0360-5302) | DOI | MR | Zbl
Cité par Sources :
