We investigate the properties of a model describing the motion of liquid drops sitting on a flat surface. Here we consider the so-called quasi-static approximation model, where the speed of the contact line between the fluid and the surface is much slower than the capillary relaxation time. We show that, under a geometric constraint on the initial configuration, the solution is globally well-posed, and the support of the solution uniformly converges to a ball. We will also discuss the asymptotic behavior of the droplet evolution on tilted surface. This is joint work with William Feldman and Antoine Mellet.