Special Session 100: Analysis of free boundary problems
Contents
We study several well-known and new free boundary problems in fluid dynamics. The main emphasis will be placed on the powerful approach that exploits direct mapping techniques (i.e.\ Hanzawa transformations) in combination with maximal regularity in an $L_p$-setting.
We discuss the advantages as well as the drawbacks of this approach and present some recent results concerning the well-posedness of the considered problems. The models studied here will range from dynamics driven by surface tension
over viscous interfaces to elasticity driven dynamics as encountered for example in biological systems formed by membranes.