1 dec 2005

**Abstract.**

Dear All,

next Thursday, 1 December, at 17:30 in ``Sala dei Seminari'' of the Department of Mathematics

Stefania Maniglia, from Department of Mathematics of Pisa, will present

``Transport equation for *log-lipschitz*
vector fields and Littlewood-Paley decomposition.''

The abstract follows.

We illustrate the results of the paper "Equations de transport relatives a` des champs de vecteurs non-lipschitziens et mecanique des fluides"
by H.Bahouri and J.-H.Chemin.
In particular, we describe (as done by the authors in their
paper) how to get an existence and uniqueness result
for measure valued solutions of the Cauchy problem for the transport equation, using the Littlewood-Paley theory and Besov spaces,
where the involved vector field is supposed to be a free-divergence vector field belonging to the space $L^1_{loc}(\R^+;LL(\R^d))$ and
$LL(\R^d)$ denotes the space of *log-lipshitz* functions.