Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
Perthame, Benoît
Journées équations aux dérivées partielles, (1997), p. 1-7 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{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},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1997},
     pages = {1-7},
     mrnumber = {1482279},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/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), pp. 1-7. http://gdmltest.u-ga.fr/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 86a:46033 | Zbl 0599.35009

[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 94m:76093 | Zbl 0860.76064

[Bd1] D. Benedetto, Convergence of velicity blobs method for the Euler Equation. Math. Methods Appl. Sc., vol. 19 (1986) 463-479. | MR 97i:76035 | Zbl 0992.76073

[Bd2] D. Benedetto, A remark on the Hamiltonian structure of the incompresible flows. J. stat. Phys. 79 (1997). | Zbl 01553944

[Bz] M. Bézard, Régularité précisée des moyennes dans les équations de transport, Bull. Soc. Math. France 22 (1994), 29-76. | Numdam | MR 95g:82083 | Zbl 0798.35025

[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 0893.35068

[D1] R. Di Perna, Convergence of the viscosity method for Isentropic Gas Dynamics, Comm. Math. Phys. 91 (1983), 1-30. | MR 85i:35118 | Zbl 0533.76071

[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 90k:82045 | Zbl 0698.45010

[DiL2] R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math. 42 (1989), 729-757. | MR 90i:35236 | Zbl 0698.35128

[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 92g:35036 | Zbl 0763.35014

[Ge] P. Gérard, Moyennisation et régularité deux-microlocale, Ann. Sci. Ecole Normale Sup. 4 (1990), 89-121. | Numdam | MR 91g:35068 | Zbl 0725.35003

[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 86m:82062 | Zbl 0591.45007

[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 89a:35179 | Zbl 0652.47031

[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 96c:35184 | Zbl 0827.35110

[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 97e:35107 | Zbl 0853.76077

[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 94d:35100 | Zbl 0820.35094

[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 91k:35156 | Zbl 0729.49007

[MP] J. H. Maddocks and R.L. Pego, An unconstrained Hamiltonian formulation for incompressible fluid flow. Comm. Math. Phys. 170 (1995) 207. | MR 96a:76085 | Zbl 0824.76021

[M] F. Murat, Compacité par compensation, Ann. Sc. Norm. Sup. Pisa 5 (1978), 489-507. | Numdam | MR 80h:46043a | Zbl 0399.46022

[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 0850.76130

[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 97f:82042 | Zbl 0857.76090

[Se] D. Serre Systemes hyperboliques de lois de conservation, Parties I et II. Diderot, Paris (1996). | MR 99b:35139 | Zbl 0930.35002

[Sm] P. Smereka. A Vlasov description of the Euler equation. Nonlinearity 9 (1996), 1361-1386. | MR 97h:76029 | Zbl 0926.76023

[Sp] H. Spohn. Large scale dynamics of interacting particles. Springer-Verlag, Berlin (1991). | Zbl 0742.76002

[St] E. M. Stein. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton (1970). | MR 44 #7280 | Zbl 0207.13501

[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 81m:35014 | Zbl 0437.35004