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The flow associated to weakly differentiable vector fields

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Martedi' 12 maggio alle ore 12 in aula 1AD/30 Gianluca Crippa (Universita' di Parma) terra' un seminario dal titolo "The flow associated to weakly differentiable vector fields".

-Abstract
I will review some of the main points of the well-posedness theory for transport and continuity equations with velocity fields whose regularity does not fit the classical Cauchy-Lipschitz framework. There are many motivations for this study, for instance applications to fluidodynamics and to conservation laws. I will also mention the connection with the well-posedness of the ordinary differential equation, through a kind of extension of the classical methods of characteristics. In the final part of the talk, I will present some recent results (obtained jointly with Giovanni Alberti and Stefano Bianchini), regarding sharp well-posedness results for the two-dimensional transport equation with a bounded divergence-free velocity field.

Rif. int. F. Ancona, M. Bardi, A. Cesaroni

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