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DTSTART;VALUE=DATE:20111122T171500
DTEND;VALUE=DATE:20111122T171500
UID:5638@agenda.unifr.ch
DESCRIPTION:In the first part of the talk I will give an overview on some recent\nadvances on the study of the continuity equation when the velocity\nfield is non-smooth. This kind of equation appears very often in\nproblems originating from the dynamics of fluids, and the lack of\nregularity of the velocity field is due "irregular" physical\nbehaviours, like shocks or turbulence. I will motivate the need for\nthe use of geometric measure theory for this kind of analysis, and I\nwill illustrate the approach based on the notion of renormalized\nsolutions used by DiPerna-Lions and by Ambrosio to study the Sobolev\nand the bounded variation cases, respectively.\n<br>\nIn the second part, I will present some results from a project in collaboration\nwith Giovanni Alberti (University of Pisa) and Stefano Bianchini\n(SISSA, Trieste). We focus on the two-dimensional case. In the\nsimplest form, our result gives a characterization of (bounded,\nautonomous and divergence-free) vector fields on the plane such that\nuniqueness for the continuity equation holds. The proof relies on a\ndimension-reduction argument which reduces the problem to a family of\none-dimensional problems. I will try to convey to the audience some\nflavour of the techniques in our proof.
SUMMARY:Gianluca Crippa: The continuity equation with non-smooth velocity field. An overview and the two-dimensional case
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5638
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