G. Alberti, G. Crippa, and &. A. Mazzucato, Exponential self-similar mixing and loss of regularity for continuity equations, Comptes Rendus Mathematique, vol.352, issue.11, pp.901-906, 2014.
DOI : 10.1016/j.crma.2014.08.021

L. Ambrosio, Transport equation and Cauchy problem for BV vector fields and applications, Journ??es ??quations aux d??riv??es partielles, vol.158, pp.227-260, 2004.
DOI : 10.5802/jedp.1
URL : http://archive.numdam.org/article/JEDP_2004____A1_0.pdf

L. Ambrosio, M. Colombo, and &. A. Figalli, On the Lagrangian structure of transport equations: the Vlasov- Poisson system, 2014.

L. Ambrosio and &. , Crippa: Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields, Lecture Notes of the UMI, vol.5, pp.3-54, 2008.

L. Ambrosio and &. G. Crippa, Continuity equations and ODE flows with non-smooth velocity. Lecture Notes of a course given at Heriot-Watt University, Edinburgh. Proceeding of the Royal Society of Edinburgh
DOI : 10.1017/s0308210513000085

L. Ambrosio, M. Lecumberry, and &. S. Maniglia, Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow, pp.29-50, 2005.

A. Bohun, F. Bouchut, and &. , Crippa: Lagrangian solutions to the Vlasov-Poisson equation with L 1 density, 2014.

A. Bohun, F. Bouchut, and &. , Crippa: Lagrangian solutions to the Euler equation with L 1 vorticity, 2014.

F. Bouchut, Renormalized Solutions to the Vlasov Equation with Coefficients of Bounded Variation, Archive for Rational Mechanics and Analysis, vol.157, issue.1, pp.75-90, 2001.
DOI : 10.1007/PL00004237

F. Bouchut and &. , Uniqueness, Renormalization, and Smooth Approximations for Linear Transport Equations, SIAM Journal on Mathematical Analysis, vol.38, issue.4, pp.1316-1328, 2006.
DOI : 10.1137/06065249X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.8745

F. Bouchut and &. G. Crippa, Equations de transportàtransport`transportà coefficient dont le gradient est donné par une intégrale sin-gulì ere. (French) [Transport equations with a coefficient whose gradient is given by a singular integral]. Séminaire: ´ Equations aux Dérivées Partielles, Exp. No. I, 15 pp., Sémin. ´ Equ. Dériv. Partielles, ´ Ecole Polytech, 2007.

F. Bouchut and &. G. Crippa, LAGRANGIAN FLOWS FOR VECTOR FIELDS WITH GRADIENT GIVEN BY A SINGULAR INTEGRAL, Journal of Hyperbolic Differential Equations, vol.10, issue.02, pp.235-282, 2013.
DOI : 10.1142/S0219891613500100
URL : https://hal.archives-ouvertes.fr/hal-00724586

A. Bressan, A lemma and a conjecture on the cost of rearrangements, Rend. Sem. Mat. Univ. Padova, vol.110, pp.97-102, 2003.

A. Bressan, An ill posed Cauchy problem for a hyperbolic system in two space dimensions, Rend. Sem. Mat. Univ. Padova, pp.110-103, 2003.

N. Champagnat and &. Jabin, Force Terms, Communications in Partial Differential Equations, vol.43, issue.5, pp.786-816, 2010.
DOI : 10.1007/s10231-003-0082-4
URL : https://hal.archives-ouvertes.fr/inria-00373784

G. Crippa, The flow associated to weakly differentiable vector fields. Theses of Scuola Normale Superiore di Pisa (New Series), 12, 2009.

G. Crippa, Ordinary Differential Equations and Singular Integrals, HYP2012 Proceedings, AIMS Book Series on Applied Mathematics, pp.109-117, 2014.

G. Crippa and &. , De Lellis: Estimates for transport equations and regularity of the DiPerna-Lions flow, J

G. Crippa and &. , De Lellis: Regularity and compactness for the DiPerna-Lions flow, HYP206 Proceedings, pp.423-430, 2008.

C. and D. Lellis, Notes on hyperbolic systems of conservation laws and transport equations. Handbook of differential equations: evolutionary equations, pp.277-382, 2007.

R. J. Diperna and &. , Lions: Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math, pp.98-511, 1989.

C. , L. Bris, and &. , Lions: Renormalized solutions of some transport equations with partially W 1,1 velocities and applications, Annali di Matematica, vol.183, pp.97-130, 2003.

N. Lerner, Transport equations with partially BV velocities, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.3, pp.681-703, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00021015

A. J. Majda, G. Majda, and &. Y. , Zheng: Concentrations in the one-dimensional Vlasov-Poisson equations. I. Temporal development and non-unique weak solutions in the single component case, Phys. D, pp.74-77, 1994.

E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, 1993.

Y. X. Zheng and &. A. , Majda: Existence of global weak solutions to one-component Vlasov-Poisson and Fokker- Planck-Poisson systems in one space dimension with measures as initial data, Comm. Pure Appl. Math, issue.10, pp.47-1365, 1994.

A. Bohun, D. Mathematik-und-informatik, U. Upem, and F. , CH- 4051, Basel, Switzerland E-mail address: anna.bohun@unibas.ch François Bouchut Marne-la-Vallée, France E-mail address: francois.bouchut@u-pem.fr Gianluca Crippa, CNRS, p.4051