Interface cinétique / fluide : Un modèle simplifié

Vasseur, Alexis

Interface cinétique / fluide : Un modèle simplifié

Vasseur, Alexis ¹

¹ Laboratoire J.A.Dieudonné, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 NICE Cedex 2

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Exposé no. 3, 15 p.

MR Zbl

Affiliations des auteurs :

Vasseur, Alexis ¹

¹ Laboratoire J.A.Dieudonné, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 NICE Cedex 2

@article{SEDP_2002-2003____A3_0,
     author = {Vasseur, Alexis},
     title = {Interface cin\'etique / fluide~: {Un} mod\`ele simplifi\'e},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:3},
     pages = {1--15},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     zbl = {02124129},
     mrnumber = {2030698},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_2002-2003____A3_0/}
}

TY  - JOUR
AU  - Vasseur, Alexis
TI  - Interface cinétique / fluide : Un modèle simplifié
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:3
PY  - 2002-2003
SP  - 1
EP  - 15
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2002-2003____A3_0/
LA  - fr
ID  - SEDP_2002-2003____A3_0
ER  -

%0 Journal Article
%A Vasseur, Alexis
%T Interface cinétique / fluide : Un modèle simplifié
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:3
%D 2002-2003
%P 1-15
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2002-2003____A3_0/
%G fr
%F SEDP_2002-2003____A3_0

Vasseur, Alexis. Interface cinétique / fluide : Un modèle simplifié. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Exposé no. 3, 15 p. http://www.numdam.org/item/SEDP_2002-2003____A3_0/

Bibliographie
Cité par

[1] Bardos, C.; le Roux, A. Y.; Nédélec, J.-C. First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, Volume 4 (1979) no. 9, pp. 1017-1034 | MR | Zbl

[2] Ben Abdallah, N.; Degond, P.; Gamba, I. M. Coupling one-dimensional time-dependent classical and quantum transport models, J. Math. Phys., Volume 43 (2002) no. 1, pp. 1-24 | MR | Zbl

[3] Bobylev, A. V.; Grzhibovskis, R.; Heintz, A. Entropy inequalities for evaporation/condensation problem in rarefied gas dynamics, J. Statist. Phys., Volume 102 (2001) no. 5-6, pp. 1151-1176 | MR | Zbl

[4] Bourdarias, C.; Gisclon, M.; Omrane, A. Transmission boundary conditions in a model-kinetic decomposition domain, Discrete Contin. Dyn. Syst. Ser. B, Volume 2 (2002) no. 1, pp. 69-94 | MR | Zbl

[5] Bourgat, J.-F.; Le Tallec, P.; Perthame, B.; Qiu, Y. Coupling Boltzmann and Euler equations without overlapping, Domain decomposition methods in science and engineering (Como, 1992) (Contemp. Math.), Volume 157, Amer. Math. Soc., Providence, RI, 1994, pp. 377-398 | MR | Zbl

[6] Brenier, Yann Une application de la symétrisation de Steiner aux équations hyperboliques : la méthode de transport et écroulement, C. R. Acad. Sci. Paris Sér. I Math., Volume 292 (1981) no. 11, pp. 563-566 | MR | Zbl

[7] Brenier, Yann Résolution d’équations d’évolution quasilinéaires en dimension $N$ d’espace à l’aide d’équations linéaires en dimension $N + 1$ , J. Differential Equations, Volume 50 (1983) no. 3, pp. 375-390 | Zbl

[8] Coron, François; Golse, François; Sulem, Catherine A classification of well-posed kinetic layer problems, Comm. Pure Appl. Math., Volume 41 (1988) no. 4, pp. 409-435 | MR | Zbl

[9] Degond, Pierre; Schmeiser, Christian Kinetic boundary layers and fluid-kinetic coupling in semiconductors, Transport Theory Statist. Phys., Volume 28 (1999) no. 1, pp. 31-55 | MR | Zbl

[10] Dellacherie, Stéphane Personal Communication

[11] Engquist, Björn; Osher, Stanley One-sided difference approximations for nonlinear conservation laws, Math. Comp., Volume 36 (1981) no. 154, pp. 321-351 | MR | Zbl

[12] Giga, Yoshikazu; Miyakawa, Tetsuro A kinetic construction of global solutions of first order quasilinear equations, Duke Math. J., Volume 50 (1983) no. 2, pp. 505-515 | MR | Zbl

[13] Golse, François Shock profiles for the Perthame-Tadmor kinetic model, Comm. Partial Differential Equations, Volume 23 (1998) no. 11-12, pp. 1857-1874 | MR | Zbl

[14] Golse, François; Perthame, Benoît; Sentis, Rémi Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d’un opérateur de transport, C. R. Acad. Sci. Paris Sér. I Math., Volume 301 (1985) no. 7, pp. 341-344 | MR | Zbl

[15] Klar, Axel Domain decomposition for kinetic problems with nonequilibrium states, European J. Mech. B Fluids, Volume 15 (1996) no. 2, pp. 203-216 | MR | Zbl

[16] Le Tallec, Patrick; Mallinger, François Coupling Boltzmann and Navier-Stokes equations by half fluxes, J. Comput. Phys., Volume 136 (1997) no. 1, pp. 51-67 | MR | Zbl

[17] Lions, P.-L.; Perthame, B.; Tadmor, E. A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc., Volume 7 (1994) no. 1, pp. 169-191 | MR | Zbl

[18] Nouri, A.; Omrane, A.; Vila, J. P. Boundary conditions for scalar conservation laws from a kinetic point of view, J. Statist. Phys., Volume 94 (1999) no. 5-6, pp. 779-804 | MR | Zbl

[19] Perthame, B.; Souganidis, P. E. A limiting case for velocity averaging, Ann. Sci. École Norm. Sup. (4), Volume 31 (1998) no. 4, pp. 591-598 | EuDML | Numdam | MR | Zbl

[20] Perthame, Benoit An introduction to kinetic schemes for gas dynamics, An introduction to recent developments in theory and numerics for conservation laws (Freiburg/Littenweiler, 1997) (Lect. Notes Comput. Sci. Eng.), Volume 5, Springer, Berlin, 1999, pp. 1-27 | MR | Zbl

[21] Perthame, Benoît; Tadmor, Eitan A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys., Volume 136 (1991) no. 3, pp. 501-517 | MR | Zbl

[22] Poupaud, F. Diffusion approximation of the linear semiconductor Boltzmann equation : analysis of boundary layers, Asymptotic Anal., Volume 4 (1991) no. 4, pp. 293-317 | MR | Zbl

[23] Sone, Yoshio; Sugimoto, Hiroshi; Aoki, Kazuo Cylindrical Couette flows of a rarefied gas with evaporation and condensation : reversal and bifurcation of flows, Phys. Fluids, Volume 11 (1999) no. 2, pp. 476-490 | MR | Zbl

[24] Tidriri, M. Oral communication

[25] Vasseur, A. Time regularity for the system of isentropic gas dynamics with $γ = 3$ ., Commun. Partial Differ. Equations, Volume 24 (1999) no. 11-12, pp. 1987-1997 | MR | Zbl

[26] Vasseur, Alexis Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with $γ = 3$ ., Indiana Univ. Math. J., Volume 48 (1999) no. 1, pp. 347-364 | MR | Zbl

[27] Vasseur, Alexis Strong traces for solutions of multidimensional scalar conservation laws, Arch. Ration. Mech. Anal., Volume 160 (2001) no. 3, pp. 181-193 | MR | Zbl