On free boundary problems with moving contact points for stationary two-dimensional Navier–Stokes equations

The solvability of the problem on a slow drying a plane capillary in a classical formulation (i.e. with the adherence condition on a rigid wall) is established. The proof is based on a detailed study of the asymptotics of the solution in the neighbourhood of the point of a contact a free boundary with a moving wall, including estimates of coefficients in well known asymptotics formulas. It is shown that the only value of a contact angle admitting the solution of the problem with a finite energy dissipation equals $\pi$. Bibliography: 18 titles.