Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques

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1. [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. Zbl0599.35009MR86a:46033
2. [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). Zbl0860.76064MR94m:76093
3. [Bd1] D. Benedetto, Convergence of velicity blobs method for the Euler Equation. Math. Methods Appl. Sc., vol. 19 (1986) 463-479. Zbl0992.76073MR97i:76035
4. [Bd2] D. Benedetto, A remark on the Hamiltonian structure of the incompresible flows. J. stat. Phys. 79 (1997). Zbl1081.76532
5. [Bz] M. Bézard, Régularité précisée des moyennes dans les équations de transport, Bull. Soc. Math. France 22 (1994), 29-76. Zbl0798.35025MR95g:82083
6. [BC] Y. Brenier, L. Corrias. A kinetic formulation for multibranch entropy solutions of scalar conservation laws. Ann. Inst. H. Poincaré analyse non-linéaire. Zbl0893.35068
7. [D1] R. Di Perna, Convergence of the viscosity method for Isentropic Gas Dynamics, Comm. Math. Phys. 91 (1983), 1-30. Zbl0533.76071MR85i:35118
8. [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. Zbl0698.45010MR90k:82045
9. [DiL2] R. J. DiPerna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math. 42 (1989), 729-757. Zbl0698.35128MR90i:35236
10. [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. Zbl0763.35014MR92g:35036
11. [Ge] P. Gérard, Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Normale Sup. 4 (1990), 89-121. Zbl0725.35003MR91g:35068
12. [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. Zbl0591.45007MR86m:82062
13. [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. Zbl0652.47031MR89a:35179
14. [HLP] H. Herero, B. Lucquin and B. Perthame. On the motion of dispersed balls in a potential flow. Raport LAN (1987). 
15. [K] G.A. Kuz'min, Ideal incompressible hydrodynamics in terms of the vortex mementum density. Phys. Lett. 96A (1983), 88. 
16. [L] P.-L. Lions, Régularité optimale des moyennes en vitesses. C. R. Acad. Sci. Paris, t. 320 Série I (1995), 911-915. Zbl0827.35110MR96c:35184
17. [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). Zbl0853.76077MR97e:35107
18. [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. Zbl0820.35094MR94d:35100
19. [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). Zbl0729.49007MR91k:35156
20. [MP] J. H. Maddocks and R.L. Pego, An unconstrained Hamiltonian formulation for incompressible fluid flow. Comm. Math. Phys. 170 (1995) 207. Zbl0824.76021MR96a:76085
21. [M] F. Murat, Compacité par compensation, Ann. Sc. Norm. Sup. Pisa 5 (1978), 489-507. Zbl0399.46022MR80h:46043a
22. [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. Zbl0850.76130
23. [PS] B. Perthame et P. E. Souganidis. A limiting case of averaging lemmas. Rapport LAN (1987). 
24. [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). Zbl0857.76090MR97f:82042
25. [Se] D. SerreSystemes hyperboliques de lois de conservation, Parties I et II. Diderot, Paris (1996). Zbl0930.35002MR99b:35139
26. [Sm] P. Smereka. A Vlasov description of the Euler equation. Nonlinearity 9 (1996), 1361-1386. Zbl0926.76023MR97h:76029
27. [Sp] H. Spohn. Large scale dynamics of interacting particles. Springer-Verlag, Berlin (1991). Zbl0742.76002
28. [St] E. M. Stein. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton (1970). Zbl0207.13501MR44 #7280
29. [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). Zbl0437.35004MR81m:35014