Journal of Mathematical Sciences

, Volume 84, Issue 1, pp 930–947

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

• V. A. Solonnikov
Article

## Abstract

Solvability of the problem of slow drying of a plane capillary in the classical setting (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 near a point of contact of the free boundary with a moving wall, including estimates of the coefficients in well known asymptotic formulas. It is shown that the only value of the contact angle admitting a solution of the problem with finite energy dissipation equals π. Bibliography: 18 titles.

### Keywords

Contact Angle Energy Dissipation Contact Point Free Boundary Boundary Problem

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