Sur les Champs de vecteurs peu réguliers
Ferruccio Colombini[1]; Nicolas Lerner[2]
- [1] Dipartimento di Matematica, Università di Pisa, Via F.Buonarroti 2, 56127 Pisa, Italia
- [2] Université de Rennes 1, Irmar, Campus de Beaulieu, 35042 Rennes cedex, France
Séminaire Équations aux dérivées partielles (2000-2001)
- Volume: 2000-2001, page 1-15
Access Full Article
topHow to cite
topColombini, Ferruccio, and Lerner, Nicolas. "Sur les Champs de vecteurs peu réguliers." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-15. <http://eudml.org/doc/11010>.
@article{Colombini2000-2001,
affiliation = {Dipartimento di Matematica, Università di Pisa, Via F.Buonarroti 2, 56127 Pisa, Italia; Université de Rennes 1, Irmar, Campus de Beaulieu, 35042 Rennes cedex, France},
author = {Colombini, Ferruccio, Lerner, Nicolas},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Vector fields; Transport equation; Weak solutions; $BV$},
language = {fre},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Sur les Champs de vecteurs peu réguliers},
url = {http://eudml.org/doc/11010},
volume = {2000-2001},
year = {2000-2001},
}
TY - JOUR
AU - Colombini, Ferruccio
AU - Lerner, Nicolas
TI - Sur les Champs de vecteurs peu réguliers
JO - Séminaire Équations aux dérivées partielles
PY - 2000-2001
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2000-2001
SP - 1
EP - 15
LA - fre
KW - Vector fields; Transport equation; Weak solutions; $BV$
UR - http://eudml.org/doc/11010
ER -
References
top- M Aizenman, On vector fields as generators of flows : a counterexample to Nelson’s conjecture, Ann. Math. 107 (1978), (2), 287-296 Zbl0394.28012
- H Bahouri, J.-Y Chemin, Équations de transport relatives à des champs de vecteurs non-lipschitziens et mécanique des fluides., Arch. Rational Mech. Anal. 127 (1994), 159-181 Zbl0821.76012MR1288809
- F Bouchut, L Desvillettes, On two-dimensional Hamiltonian transport equations with continuous coefficients, Diff. and Int. Eq. 14 (2001), 1015-1024 Zbl1028.35042MR1827101
- F Bouchut, F James, One dimensional transport equations with discontinuous coefficients, Non linear analysis 32 (1998), 891-933 Zbl0989.35130MR1618393
- F Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. for Ration. Mech. and Anal. (à paraître) Zbl0979.35032MR1822415
- J.-Y Chemin, N Lerner, Flot de champ de vecteurs non lipschitziens et équations de Navier-Stokes, J.Differ. Eq. 121 (1995), 314-328 Zbl0878.35089MR1354312
- F Colombini, N Lerner, Hyperbolic equations with non Lipschitz coefficients, Duke Math.J. 77 (1995), 657-698 Zbl0840.35067MR1324638
- F Colombini, N Lerner, Uniqueness of continuous solutions for vector fields, Duke Math.J.(à paraître) Zbl1017.35029MR1882138
- B Desjardins, A few remarks on ordinary differential equations, Comm.PDE 21 (1996), 1667-1703 Zbl0899.35022MR1421208
- B Desjardins, Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations, Diff. & Integ. Equ. 10 (1995), 3, 577-586 Zbl0902.76028MR1744862
- B Desjardins, Global existence results for the incompressible density-dependent Navier-Stokes equations in the whole space, Diff. & Integ. Equ. 10 (1995), 3, 587-598 Zbl0902.76027MR1744863
- R.J. DiPerna, P.L Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547 Zbl0696.34049MR1022305
- H Federer, Geometric measure theory, Grund. der math. Wiss. 153 (1969), Springer-Verlag Zbl0176.00801
- T.M Flett, Differential analysis, (1980), Cambridge Univ. Press Zbl0442.34002MR561908
- N Bourbaki, Fonctions d’une variable réelle, (1976), C.C.L.S., Paris Zbl0346.26003
- L Hörmander, The Analysis of Linear PDO, Grund. der math. Wiss. 256-257-274-275 (1983-85), Springer-Verlag
- L Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathématiques et applications 26 (1996), Springer-Verlag Zbl0881.35001MR1466700
- Y Hu, N Lerner, On the existence and uniqueness of solutions to stochastic equations in infinite dimensions with integral-Lipschitz coefficients, preprint 00-39, Irmar (2000) Zbl1037.60060MR1967224
- P.L Lions, Sur les équations différentielles ordinaires et les équations de transport, C.R. Acad.Sc. Paris, Série I, 326 (1998), 833-838 Zbl0919.34028MR1648524
- G Petrova, B Popov, Linear transport equations with discontinuous coefficients, Comm.PDE 24 (1999), 1849-1873 Zbl0992.35104MR1708110
- F Poupaud, M Rascle, Measure solutions to the linear multidimensional transport equation with non-smooth coefficients, Comm.PDE 22 (1997), 337-358 Zbl0882.35026MR1434148
- X.Saint Raymond, L’unicité pour les problèmes de Cauchy linéaires du premier ordre, Enseign. Math. no. 1-2, (2), 32 (1986), 1-55 Zbl0625.35009
- F Treves, Topological vector spaces, distributions and kernels, Pure & Appl. Math.Ser. (1967), Academic Press Zbl0171.10402MR225131
- A.I Vol’pert, The space and quasi-linear equations, Math.USSR Sbornik 2 (1967), 225-267 Zbl0168.07402
- W.P Ziemer, Weakly differentiable functions, Graduate texts in mathematics 120 (1989), Springer-Verlag Zbl0692.46022MR1014685
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.