Dear Colleagues,
we would like to invite you to the following seminar by Jules Pitcho (UZH) to be held this Wednesday (May 4th) at Dipartimento di Matematica in Pisa and online via Google Meets.
The organizers,
A. Agazzi and F. Grotto
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Time:
May 4th, 2022, 14:00-15:00 CET
Speaker: Jules Pitcho (UZH - Universität Zürich)
Title: Since the work of Di Perna-Lions and Ambrosio, it is known that the continuity equation with divergence-free Sobolev vector field is well-posed for densities with suitable integrability. At the Lagrangian level, these works translate into a selection
principle for integral curves under which uniqueness for almost every initial data is true. Nevertheless, uniqueness of integral curves can fail almost everywhere. The deterministic technique used to construct such divergence-free Sobolev vector fields and
non-unique integral curves go by the name of convex integration: we will explain some of the ideas underlying this technique. We will conclude by arguing that for rougher vector fields, a genuinely stochastic behaviour of integral curves is to be expected:
we should not hope for an almost everywhere selection principle for integral curves.