Abstract: | One considers the problem of the plane motion of a viscous incompressible fluid which fills partially a container V, bounded by the straight line 1 = {x:x
2 = 0} and the contour ( V![setmn](/content/nhvt462v67614634/xxlarge8726.gif) 1), consisting of two semilines (1) = {x:x
1<–1,x
2 = h0} (2) = {x:x
1 = 0,x
2 h0+1} joined by a smooth curvel
(3). One assumes that the motion is due to a nonzero flow and by the motion of the lower wall 1 with a constant velocity R 0. The unique solvability of this problem is proved for small R and .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 174–179, 1981.In conclusion, the author expresses his deep gratitude to V. A. Solonnikov for his guidance. |