Seminar series
Date
Mon, 09 May 2011
17:00
17:00
Location
Gibson 1st Floor SR
Speaker
Giovanni Alberti
Organisation
Universita di Pisa
We give a characterization of divergence-free vector fields on the plane such that the Cauchy problem for the associated continuity (or transport) equation has a unique bounded solution (in the sense of distribution).
Unlike previous results in this directions (Di Perna-Lions, Ambrosio), the proof relies on a dimension-reduction argument, which can be regarded as a variant of the method of characteristics. Note that our characterization is not stated in terms of function spaces, but is based on a suitable weak formulation of the Sard property for the potential associated to the vector-field.
This is a joint work with S. Bianchini (SISSA, Trieste) and Gianluca Crippa (Parma).