Seminar on Analysis, Geometry and PDEs - Gabriele Brüll (Lund University)
Non-Newtonian two-phase thin-film problem
Speaker: Gabriele Brüll (Lund University)
Abstract: In this talk, I will discuss the modeling and some analysis of a two-phase thin-film equation, where one of the fluids is Newtonian while the other one is a non-Newtonian Ellis fluid. The system of evolution equations is derived from the Navier–Stokes equations by lubrication approximation and cross-secional averaging. The system is degenerate, strongly coupled, parabolic and of fourth order with merely Hölder-continuous dependence on the coefficients. For the case of strictly positive initial film heights, local existence of strong solutions is proved by abstract semigroup theory and uniqueness by energy methods. Moreover, asymptotic stability of steady states is investigated.
The talk is based on a joint work with O. Assenmacher and C. Lienstromberg.
Tid: 2022-05-31 15:15 till 16:15
eskil [dot] rydhe [at] math [dot] lu [dot] se