A free boundary problem for the stokes system with contact lines
Marco A. Fontelos, Juan J. L. Velázquez · Communications in Partial Differential Equations · 1998
In this paper we study an evolution free boundary problem for the two-dimensional Stoltes system in the case in which the free boundary intersects the solid boundary of a container. We prove existence and uniqueness of solutionsfor this problem in suitable classes of functions and under suitable smallness conditions for the initial data. For these solutions the contact point moves with an uniform velocity with respect to the container.