Uniqueness and Nonuniqueness for Nonsmooth Divergence Free Transport
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Exposé no. 22, 21 p.
Colombini, Ferrucio 1 ; Luo, Tao 2 ; Rauch, Jeffrey 3

1 Dipartimento di Matematica, Università di Pisa, Pisa, Italia
2 Department of Mathematics, Georgetown University, Washington DC 20057,USA
3 Department of Mathematics, University of Michigan, Ann Arbor 48104 MI, USA
@article{SEDP_2002-2003____A22_0,
     author = {Colombini, Ferrucio and Luo, Tao and Rauch, Jeffrey},
     title = {Uniqueness and {Nonuniqueness} for {Nonsmooth} {Divergence} {Free} {Transport}},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:22},
     pages = {1--21},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     zbl = {1065.35089},
     mrnumber = {2030717},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2002-2003____A22_0/}
}
TY  - JOUR
AU  - Colombini, Ferrucio
AU  - Luo, Tao
AU  - Rauch, Jeffrey
TI  - Uniqueness and Nonuniqueness for Nonsmooth Divergence Free Transport
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:22
PY  - 2002-2003
SP  - 1
EP  - 21
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2002-2003____A22_0/
LA  - en
ID  - SEDP_2002-2003____A22_0
ER  - 
%0 Journal Article
%A Colombini, Ferrucio
%A Luo, Tao
%A Rauch, Jeffrey
%T Uniqueness and Nonuniqueness for Nonsmooth Divergence Free Transport
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:22
%D 2002-2003
%P 1-21
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2002-2003____A22_0/
%G en
%F SEDP_2002-2003____A22_0
Colombini, Ferrucio; Luo, Tao; Rauch, Jeffrey. Uniqueness and Nonuniqueness for Nonsmooth Divergence Free Transport. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Exposé no. 22, 21 p. http://www.numdam.org/item/SEDP_2002-2003____A22_0/

[1] M. Aizenman, On vector fields as generators of flows: a counterexample to Nelson’s conjecture, Ann. Math. 107 (1978), 287-296. | Zbl

[2] G. Alberti, Rank-one properties for derivatives of functions with bounded variation, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 239-274. | MR | Zbl

[3] L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, preprint Scuola Norm. Sup. Pisa, March 2003. | MR | Zbl

[4] M. Beals, Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems, Birkhäuser, Boston, 1989. | MR | Zbl

[5] F. Bouchut, Renormalized solutions to the Vlasov equation with coefficients of bounded variation, Arch. Rational Mech. Anal. 157 (2001), 75-90. | MR | Zbl

[6] F. Bouchut, F. James, One-dimensional transport equations with discontinuous coefficients, Nonlinear Anal. 32 (1998), 891-933. | MR | Zbl

[7] F. Colombini, N. Lerner, Uniqueness of continuous solutions for BV vector fields, Duke Math. J. 111 (2002), 357-384. | MR | Zbl

[8] F. Colombini, N. Lerner, Sur les champs de vecteurs peu réguliers, Séminaire E.D.P., Ecole Polytechnique, 2000-2001, XIV 1-15. | Numdam | MR

[9] F. Colombini, N. Lerner, Uniqueness of L solutions for a class of conormal BV vector fields, Preprint Univ. Rennes 1, February 2003. | MR | Zbl

[10] N. Depauw, Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d’un hyperplan, C.R.Acad.Sci.Paris Sér.I Math. to appear. | Zbl

[11] R.J. Di Perna, P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547. | MR | Zbl

[12] P.-L. Lions, Sur les équations différentielles ordinaires et les équations de transport, C.R.Acad.Sci.Paris Sér.I Math. 326 (1998), 833-838. | MR | Zbl

[13] E. Nelson, Les écoulements incompressibles d’énergie finie, Les Equations aux Dérivées Partielles (Paris 1962), Colloques Internationaux du C.N.R.S., 117 (1963), 159-165. | Zbl

[14] G. Petrova, B. Popov, Linear transport equations with discontinuous coefficients, Comm. PDE 24 (1999), 1849-1873. | MR | Zbl

[15] F. Poupaud, M. Rascle, Measure solutions to the linear multi- dimensional transport equation with non-smooth coefficients, Comm. PDE 22 (1997), 337-358. | MR | Zbl