# Transport equations

### Published/accepted papers

- On the Lagrangian structure of transport equations: the Vlasov-Poisson system(with L. Ambrosio and M. Colombo)

*Duke Math. J.* 166 (2017), no. 18, 3505-3568.
- Existence and uniqueness of maximal regular flows for non-smooth vector fields (with L. Ambrosio and M. Colombo)

*Arch. Ration. Mech. Anal.* 218 (2015), no. 2, 1043-1081.
- WKB analysis of Bohmian dynamics (with C. Klein, P. Markowich, and C. Sparber)

*Comm. Pure Appl. Math.* 67 (2014), no. 4, 581-620.
- A global existence result for the semigeostrophic equations in three dimensional convex domains (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Discrete Contin. Dyn. Syst.* 34 (2014), no. 4, 1251-1268.
- Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (with L. Ambrosio, M. Colombo, and G. De Philippis)

*Comm. Partial Differential Equations* 37 (2012), no. 12, 2209-2227.
- Semiclassical limit for mixed states with singular and rough potentials (with M. Ligabò and T. Paul)

*Indiana Univ. Math. J.* 61 (2012), no. 1, 193-222.
- Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (with L. Ambrosio, G. Friesecke, J. Giannoulis, and T. Paul)

*Comm. Pure Appl. Math.* 64 (2011), no. 9, 1199-1242.
- Almost everywhere well-posedness of continuity equations with measure initial data (with L. Ambrosio)

*C. R. Math. Acad. Sci. Paris* 348 (2010), no. 5-6, 249-252.
- Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (with L. Ambrosio, G. Crippa, and L. V. Spinolo)

*SIAM J. Math. Anal.* 41 (2009), no. 5, 1890-1920.
- On flows associated to Sobolev vector fields in Wiener spaces: an approach à la DiPerna-Lions (with L. Ambrosio)

*J. Funct. Anal.* 256 (2009), no.1, 179-214.

### Lectures notes and reviews

- Existence and uniqueness results for the continuity equation and applications to the chromatography system (with L. Ambrosio, G. Crippa and L. V. Spinolo)

Nonlinear conservation laws and applications, 195-204, *IMA Vol. Math. Appl.* 153, Springer, New York, 2011.
- Almost everywhere well-posedness of continuity equations with measure initial data (with L. Ambrosio)

*C. R. Math. Acad. Sci. Paris* 348 (2010), no. 5-6, 249-252.
- Optimal transport, Euler equations, Mather and DiPerna-Lions theories.

Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009