Journal of Soviet Mathematics

, Volume 25, Issue 1, pp 927–931 | Cite as

Solvability of a problem on the plane motion of a viscous incompressible fluid with a free noncompact boundary

  • K. I. Piletskas
Article
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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:x2 = 0} and the contour (∂V∖∑1), consisting of two semilines ℓ(1) = {x:x1<−1,x2 = h0} ℓ(2) = {x:x1 = 0,x2⩾h0+1} joined by a smooth curvel(3). One assumes that the motion is due to a nonzero flow ℱ 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 ℱ.

Keywords

Constant Velocity Plane Motion Incompressible Fluid Lower Wall Unique Solvability 

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© Plenum Publishing Corporation 1984

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  • K. I. Piletskas

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