The speaker: Professor Maria Specovius (Universität Kassel, Germany).
Title of the talk: "Some special aspects on the decomposition of vector fields".
Time: Thursday, 25 of April 2024, 15:00 - 16:00.
Abstract: The decompositions of vector fields into a divergence free part and a gradient field play a fundamental role in the theory of the continuum mechanics, in particular for the Navier- Stokes system. They are closely related to boundary value problems for the Laplace equation and still objects of recent research, lately in particular in unbounded domains and domains with nonsmooth boundaries. Of course, it is not possible to give a complete overview on more than thousand publications on this subject in one lecture. The purpose of this lecture is to outline some of the general principles, in particular for domains with more or less explicitly given boundary singularities. In particular for so called model problems it is astonishingly easy to combine well known results with duality arguments to get a bunch of decomposition results.