Geodesic
On free boundary problems with moving contact points for stationary two-dimensional Navier–Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 179-205 
V. A. Solonnikov. On free boundary problems with moving contact points for stationary two-dimensional Navier–Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 179-205. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a10/
@article{ZNSL_1994_213_a10,
     author = {V. A. Solonnikov},
     title = {On free boundary problems with moving contact points for stationary two-dimensional {Navier{\textendash}Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {179--205},
     year = {1994},
     volume = {213},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a10/}
}
TY  - JOUR
AU  - V. A. Solonnikov
TI  - On free boundary problems with moving contact points for stationary two-dimensional Navier–Stokes equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1994
SP  - 179
EP  - 205
VL  - 213
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a10/
LA  - ru
ID  - ZNSL_1994_213_a10
ER  - 
%0 Journal Article
%A V. A. Solonnikov
%T On free boundary problems with moving contact points for stationary two-dimensional Navier–Stokes equations
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 179-205
%V 213
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a10/
%G ru
%F ZNSL_1994_213_a10

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.