Functional setting for unsteady problems in moving domains and applications
P. Nägele, Michael Růžička, Daniel Lengeler · Complex Variables and Elliptic Equations · 2016
In this paper we develop a functional framework for unsteady problems for monotone operators in domains with smoothly moving boundaries. This is motivated by the motion of generalized Newtonian fluids in such domains. A crucial step towards this is the proof of a general integration by-parts formula for functions in non-cylindrical domains. The framework is used to show the existence of weak solutions for the p-Stokes problem in non-cylindrical domains.