%0 Journal Article %D 2014 %T A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %X 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. %I European Mathematical Society; Springer Verlag %G en %U http://urania.sissa.it/xmlui/handle/1963/34692 %1 34906 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:07:51Z No. of bitstreams: 1 Alberti_Bianchini_Crippa_52M.pdf: 318780 bytes, checksum: 556a1d21b44c58d90201b25b2c104744 (MD5) %R 10.4171/JEMS/431