On free boundary problems with moving contact points for the stationary two-dimensional Navier-Stokes equations
The solvability of the problem of a slow drying of a plane capillary in a classical formulation (with adherence condition on the rigid wall) is established. The proof is based on a detailed study of the asymptotics of the solution in the neighbourhood of a contact point of the free boundary with the moving wall, including estimates of coefficients in well known asymptotic formulas. It is shown that the solution of the problem with finite dissipation energy exists only when the contact angle equals \(\pi \).
scientific article; zbMATH DE number 996213