Mots-clés : Vector fields, Transport equation, Weak solutions, $BV$
@article{SEDP_2000-2001____A14_0, author = {Colombini, Ferruccio and Lerner, Nicolas}, title = {Sur les {Champs} de vecteurs peu r\'eguliers}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:14}, pages = {1--15}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2000-2001}, zbl = {1069.35504}, mrnumber = {1860686}, language = {fr}, url = {http://archive.numdam.org/item/SEDP_2000-2001____A14_0/} }
TY - JOUR AU - Colombini, Ferruccio AU - Lerner, Nicolas TI - Sur les Champs de vecteurs peu réguliers JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:14 PY - 2000-2001 SP - 1 EP - 15 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2000-2001____A14_0/ LA - fr ID - SEDP_2000-2001____A14_0 ER -
%0 Journal Article %A Colombini, Ferruccio %A Lerner, Nicolas %T Sur les Champs de vecteurs peu réguliers %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:14 %D 2000-2001 %P 1-15 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2000-2001____A14_0/ %G fr %F SEDP_2000-2001____A14_0
Colombini, Ferruccio; Lerner, Nicolas. Sur les Champs de vecteurs peu réguliers. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 14, 15 p. http://archive.numdam.org/item/SEDP_2000-2001____A14_0/
[Ai] On vector fields as generators of flows : a counterexample to Nelson’s conjecture, Ann. Math., Volume 107 (1978), pp. (2), 287-296 | MR | Zbl
[BC] Équations de transport relatives à des champs de vecteurs non-lipschitziens et mécanique des fluides., Arch. Rational Mech. Anal., Volume 127 (1994) no. 2, pp. 159-181 | MR | Zbl
[BD] On two-dimensional Hamiltonian transport equations with continuous coefficients, Diff. and Int. Eq., Volume 14 (2001), pp. 1015-1024 | MR | Zbl
[BJ] One dimensional transport equations with discontinuous coefficients, Non linear analysis, Volume 32 (1998), pp. 891-933 | MR | Zbl
[Bo] Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. for Ration. Mech. and Anal. (à paraître) | MR | Zbl
[ChL] Flot de champ de vecteurs non lipschitziens et équations de Navier-Stokes, J.Differ. Eq., Volume 121 (1995), pp. 314-328 | MR | Zbl
[CoL1] Hyperbolic equations with non Lipschitz coefficients, Duke Math.J., Volume 77 (1995) no. 3, pp. 657-698 | MR | Zbl
[CoL2] Uniqueness of continuous solutions for vector fields, Duke Math.J.(à paraître) | MR | Zbl
[De1] A few remarks on ordinary differential equations, Comm.PDE, Volume 21 (1996), pp. 1667-1703 | MR | Zbl
[De2] Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations, Diff. & Integ. Equ., Volume 10 (1995), pp. 3, 577-586 | MR | Zbl
[De3] Global existence results for the incompressible density-dependent Navier-Stokes equations in the whole space, Diff. & Integ. Equ., Volume 10 (1995), pp. 3, 587-598 | MR | Zbl
[DL] Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., Volume 98 (1989), pp. 511-547 | MR | Zbl
[Fe] Geometric measure theory, Grund. der math. Wiss., Volume 153, Springer-Verlag, 1969 | Zbl
[Fl] Differential analysis, Cambridge Univ. Press, 1980 | MR | Zbl
[FVR] Fonctions d’une variable réelle, C.C.L.S., Paris, 1976
[H1] The Analysis of Linear PDO, Grund. der math. Wiss., Volume 256-257-274-275, Springer-Verlag, 1983-85
[H2] Lectures on nonlinear hyperbolic differential equations, Mathématiques et applications, Volume 26, Springer-Verlag, 1996 | MR | Zbl
[HL] On the existence and uniqueness of solutions to stochastic equations in infinite dimensions with integral-Lipschitz coefficients, preprint 00-39, Irmar (2000) | MR | Zbl
[Li] Sur les équations différentielles ordinaires et les équations de transport, C.R. Acad.Sc. Paris, Série I,, Volume 326 (1998), pp. 833-838 | MR | Zbl
[PP] Linear transport equations with discontinuous coefficients, Comm.PDE, Volume 24 (1999), pp. 1849-1873 | MR | Zbl
[PR] Measure solutions to the linear multidimensional transport equation with non-smooth coefficients, Comm.PDE, Volume 22 (1997), pp. 337-358 | MR | Zbl
[Sa] L’unicité pour les problèmes de Cauchy linéaires du premier ordre, Enseign. Math. no. 1-2, (2),, Volume 32 (1986), pp. 1-55 | Zbl
[Tr] Topological vector spaces, distributions and kernels, Pure & Appl. Math.Ser., Academic Press, 1967 | MR | Zbl
[Vo] The space and quasi-linear equations, Math.USSR Sbornik, Volume 2 (1967), pp. 225-267 | Zbl
[Zi] Weakly differentiable functions, Graduate texts in mathematics, Volume 120, Springer-Verlag, 1989 | MR | Zbl