A Problem on a Viscous Layer Deformation

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The axisymmetric motion of a viscous incompressible fluid in a layer bounded by a solid plane and the free surface parallel to it is considered. There are three regimes of motion in the problem: stabilization to rest, collapse in a finite time, and an intermediate self-similar regime in which the viscous layer expands unlimitedly in an infinite time.

Original languageEnglish
Pages (from-to)60-63
Number of pages4
JournalDoklady Physics
Issue number2
Publication statusPublished - 1 Feb 2020


  • collapse of solution
  • comparison theorem
  • free boundaries
  • Lyapunov functional
  • Navier–Stokes equations


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