Solvability of some two-dimensional quasistationary free boundary problems for the Havier–Stokes equations with moving contact points

The paper is concerned with some quasistationary two-dimensional free boundary problems of viscous flow with moving contact points and with a contact angle equal $\pi$. The typical example of such a flow is filling of a capillary tube in the presence of surface tension. The proof of the solvability of these problems is based on the analysis of the asymptotic formulas for the solutions of the Havier–Stokes equations in the neighbourhood of contact points obtained by the author and V. V. Pakhnachov about 10 years ago. Bibliography: 10 titles.