A well-posed model for dynamic contact angles
The author analyzes mathematically the instationary physical system consisting of a fluid having a fixed boundary (fluid-solid interface) and a free boundary (fluid-air interface). Both boundaries intersect under the so-called contact angle. First, the author shows that in the three-dimensional case the energy dissipation along the contact line completely determines the equation for the contact angle. In particular, the vanishing energy dissipation implies the constant contact angle. Then the dynamical equations are investigated for constant contact angle in two dimensions, in the particular case of rectangular cavity. Generally, the velocity \(v\) does not belong to \(C^1\), but, using symmetric extension of variables, the author shows that \(v\in H^s\), \(1< s< 2\) (for stationary equations). This regularity and a construction due to \textit{M. Renardy} [Commun. Partial Differ. Equations 17, No. 7-8, 1387-1405 (1992; Zbl 0767.35061)] allow to establish the well-posedness of the nonlinear non-steady free boundary problem.
nonlinear non-steady free boundary problem
scientific article; zbMATH DE number 1539295