  We give a short overview on new methods for non-linear dynamic problems in
continuum mechanics developed recently in (Benesova, Kampschulte, Schwarzacher
2020, arXive:2008.04796). We describe the general idea of how to treat such
problems starting from the energetic point of view and discuss some related
recent and future results. Further we introduce an example that models the
breathing through masks: An incompressible fluid governed by the Navier-Stokes
equation is interacting with a porous, visco-elastic bulk solid. For that model
we prove the existence of a weak solution via the new methods.
