Wednesday, October 24, 2018 - 12:15
Mercoledi 24 ottobre, ore 12.15, Aula Seminari (Pal. E, RM004)
Manuel Gnann Center for Mathematics, Technical University of Munich
Analysis of moving contact line motion Abstract: We consider a lubrication approximation of the Navier-Stokes equations, known as thin-film equation, modeling the motion of a three-dimensional viscous thin fluid film. We are specifically interested in the movement of the contact line, that is, the triple junction separating the three phases liquid, gas, and solid. The understanding of the singular behavior of solutions at the contact line is of physical interest since it is linked to different physical assumptions at the triple junction and at the liquid-solid interface. Mathematically this leads to the question regarding regularity of a degenerate-parabolic fourth-order free boundary problem, for which a comparison principle is violated. By deriving suitable estimates in weighted Sobolev spaces, we are able to prove existence and uniqueness of solutions and to characterize the contact-line singularity to leading orders. Most of the talk is based on a joint publication with Mircea Petrache, Santiago de Chile (see https://doi.org/10.1016/j.jde.2018.07.015).