Transport equations

Published/accepted papers

  1. 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.
  2. 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.
  3. WKB analysis of Bohmian dynamics (with C. Klein, P. Markowich, and C. Sparber)
    Comm. Pure Appl. Math. 67 (2014), no. 4, 581-620.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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

  1. 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.
  2. 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.
  3. Optimal transport, Euler equations, Mather and DiPerna-Lions theories.
    Mémoire d'Habilitation à Diriger de Recherche (HDR). Nice, 2009