Variational approaches to dynamical problems in continuum mechanics

Continuum mechanics has always been a rich source of inspiration for many areas of analysis. The problems studied there are often highly non-trivial, yet by their very nature inherently geometrical, possessing natural estimates. At the same time many questions in continuum mechanics have been strongly linked to the calculus of variations, in particular the analysis of static and quasistatic problems in solid mechanics. Far less common, however, are variational results for dynamic problems involving inertia.

The aim of this talk is to present an overview over some recent results (obtained together with B. Benešová, S.Schwarzacher and many others), which extend previous considerations from quasistatic problems to those involving inertia. These allow us to tackle questions of existence even for highly non-linear problems such as those of fluid-structure interaction, where not even the domain of the equations is known a-priori. In addition to that, these methods also reveal a lot about the geometry of the problem, both in the physical space, as well as the abstract state-space.

At the same time this talk will serve as a high-level overview and an invitation to a corresponding class on "Variationelle Methoden in der Kontinuumsmechanik/Variational methods in continuum mechanics" during the second half of this semester. In this class we will go through these results and the required tools in more detail. Thus all interested students are explicitly invited to attend both.