Dipartimento di Scienze di Base e Applicate per l'Ingegneria

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).