TY - JOUR
T1 - A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday
Y1 - 2014
A1 - Giovanni Alberti
A1 - Stefano Bianchini
A1 - Gianluca Crippa
AB - 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.
PB - European Mathematical Society; Springer Verlag
UR - http://urania.sissa.it/xmlui/handle/1963/34692
U1 - 34906
U2 - Mathematics
U4 - 1
ER -