%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
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%R 10.4171/JEMS/431