Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
Journées équations aux dérivées partielles (1997), article no. 13, 7 p. 
@incollection{JEDP_1997____A13_0,
     author = {Perthame, Beno{\^\i}t},
     title = {Un cas limite de lemmes de compacit\'e en moyenne motiv\'e par la formulation cin\'etique de syst\`emes hyperboliques},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {13},
     pages = {1--7},
     publisher = {Ecole polytechnique},
     year = {1997},
     mrnumber = {1482279},
     language = {fr},
     url = {http://www.numdam.org/item/JEDP_1997____A13_0/}
}
TY  - JOUR
AU  - Perthame, Benoît
TI  - Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
JO  - Journées équations aux dérivées partielles
PY  - 1997
SP  - 1
EP  - 7
PB  - Ecole polytechnique
UR  - http://www.numdam.org/item/JEDP_1997____A13_0/
LA  - fr
ID  - JEDP_1997____A13_0
ER  - 
%0 Journal Article
%A Perthame, Benoît
%T Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
%J Journées équations aux dérivées partielles
%D 1997
%P 1-7
%I Ecole polytechnique
%U http://www.numdam.org/item/JEDP_1997____A13_0/
%G fr
%F JEDP_1997____A13_0
Perthame, Benoît. Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques. Journées équations aux dérivées partielles (1997), article  no. 13, 7 p. http://www.numdam.org/item/JEDP_1997____A13_0/

[Ag] V. I. Agoshkov, Spaces of functions with differential-difference characteristics and smoothness of solutions of the transport equation. Soviet Math. Dokl. 29 (1984), 662-666. | MR | Zbl

[Bu] T.F. Buttke, Velicity methods : Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flows. In Vortex flow and related numerical methods ed. J. T. Beale, G. H. Cottet and S. Huberson (Dordrecht : Kluwer) (1993). | MR | Zbl

[Bd1] D. Benedetto, Convergence of velicity blobs method for the Euler Equation. Math. Methods Appl. Sc., vol. 19 (1986) 463-479. | MR | Zbl

[Bd2] D. Benedetto, A remark on the Hamiltonian structure of the incompresible flows. J. stat. Phys. 79 (1997). | Zbl

[Bz] M. Bézard, Régularité précisée des moyennes dans les équations de transport, Bull. Soc. Math. France 22 (1994), 29-76. | Numdam | MR | Zbl

[BC] Y. Brenier, L. Corrias. A kinetic formulation for multibranch entropy solutions of scalar conservation laws. Ann. Inst. H. Poincaré analyse non-linéaire. | Numdam | Zbl

[D1] R. Di Perna, Convergence of the viscosity method for Isentropic Gas Dynamics, Comm. Math. Phys. 91 (1983), 1-30. | MR | Zbl

[DiL1] R. J. Diperna and P.-L. Lions, On the Cauchy problem for the Boltzmann Equation : global existence and weak stability results, Ann. Math. 130 (1989), 321-366. | MR | Zbl

[DiL2] R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math. 42 (1989), 729-757. | MR | Zbl

[DiLM] R. J. Diperna, P.-L. Lions and Y. Meyer, Lp regularity of velocity averages, Ann. Inst. H. Poincaré Ann. Non Linéaire 8 (1991), 271-287. | Numdam | MR | Zbl

[Ge] P. Gérard, Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Normale Sup. 4 (1990), 89-121. | Numdam | MR | Zbl

[GPS] F. Golse, B. Perthame and R. Sentis. Un résultat de compacité pour les équations du transport ..., C. R. Acad. Sci. Paris Série I 301 (1985), 341-344. | MR | Zbl

[GLPS] F. Golse, P.-L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation. J. Funct. Anal., 76 (1988), 110-125. | MR | Zbl

[HLP] H. Herero, B. Lucquin and B. Perthame. On the motion of dispersed balls in a potential flow. Raport LAN (1987).

[K] G.A. Kuz'Min, Ideal incompressible hydrodynamics in terms of the vortex mementum density. Phys. Lett. 96A (1983), 88.

[L] P.-L. Lions, Régularité optimale des moyennes en vitesses. C. R. Acad. Sci. Paris, t. 320 Série I (1995), 911-915. | MR | Zbl

[LPS] P.L. Lions, B. Perthame, P.E. Souganidis. Existence of entropy solutions to isentropic gas dynamics system. C.P.A.M. Vol. 49, 599-638 (1996). | MR | Zbl

[LPT1] P. L. Lions, B. Perthame and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. of AMS 7 (1994), 169-191. | MR | Zbl

[LPT2] P. L. Lions, B. Perthame, E. Tadmor. Formulation cinétique des lois de conservation scalaires. C.R. Acad. Sc. Paris, t. 312 Série I (1991). | MR | Zbl

[MP] J. H. Maddocks and R.L. Pego, An unconstrained Hamiltonian formulation for incompressible fluid flow. Comm. Math. Phys. 170 (1995) 207. | MR | Zbl

[M] F. Murat, Compacité par compensation, Ann. Sc. Norm. Sup. Pisa 5 (1978), 489-507. | Numdam | MR | Zbl

[O] V.I. Oseledets. On a new way of writing the Navier-Stokes equation : the Hamiltonian formalism. Comm. Moscow Math. Soc. (1988) ; translated in Russ. Math. Surveys 44 (1989), 210-211. | Zbl

[PS] B. Perthame et P. E. Souganidis. A limiting case of averaging lemmas. Rapport LAN (1987).

[RS] G. Russo and P. Smereka. Kinetic theory for bubbly flow I : collisionless case. SIAM J. Appl. Math., Vol. 56, n°2, 327-357 (1996). | MR | Zbl

[Se] D. Serre Systemes hyperboliques de lois de conservation, Parties I et II. Diderot, Paris (1996). | MR | Zbl

[Sm] P. Smereka. A Vlasov description of the Euler equation. Nonlinearity 9 (1996), 1361-1386. | MR | Zbl

[Sp] H. Spohn. Large scale dynamics of interacting particles. Springer-Verlag, Berlin (1991). | Zbl

[St] E. M. Stein. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton (1970). | MR | Zbl

[Ta] L. Tartar, Compensated compactness and applications to partial differential equations, in Research Notes in Mathematics, Nonlinear Analysis and Mechanics : Herriot-Watt Symposium Vol. 4, ed. R.J. Knops, Pitman Press (1979). | MR | Zbl