@article {2014,
title = {A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday},
number = {Journal of the European Mathematical Society;Volume 16; issue 2; pp. 201-234;},
year = {2014},
publisher = {European Mathematical Society; Springer Verlag},
abstract = {We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.},
doi = {10.4171/JEMS/431},
url = {http://urania.sissa.it/xmlui/handle/1963/34692},
author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa}
}