| Abstract: | The model problem of the plane slow steady-state motion of a viscous incompressible fluid with a free boundary is investigated. It is assumed that the free boundary does not have any points in common with the solid surfaces confining the fluid. By the solution of the auxiliary fixed-boundary problem for the Navier-Stokes equations the problem is reduced to an operator equation describing the form of the free surface. The existence and uniqueness problems for the solution and its qualitative behavior are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 91–102, May–June, 1972.In conclusion, the authors would like to thank R. M. Garipov and V. Kh. Izakson for affording an opportunity to become acquainted with the results of their unpublished work. |
