Calculus of Variations and Geometric Measure Theory
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Transport equation for /log-lipschitz/ vector fields and Littlewood-Paley decomposition.

Stefania Maniglia (Dip. Mat. Univ. Lecce)

created by magnani on 25 Nov 2005
modified on 01 Dec 2005

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.

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