01084nas a2200133   4500008004100000245014200041210006900183260005100252520053000303100002200833700002300855700002100878856005100899       2014                        en  d00aA uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday0 auniqueness result for the continuity equation in two dimensions   bEuropean Mathematical Society; Springer Verlag3 aWe 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.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca  uhttp://urania.sissa.it/xmlui/handle/1963/34692