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

Voir la notice de l'article 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. 
@article{ZNSL_1994_213_a10,
     author = {V. A. Solonnikov},
     title = {On free boundary problems with moving contact points for stationary two-dimensional {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {179--205},
     publisher = {mathdoc},
     volume = {213},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a10/}
}
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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/