FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 1, PAGES 67-84

A. S. Demidov

O. A. Vasilieva

Abstract

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A model destined for investigation of the causes of some peculiarities of
the classical Stokes--Leibenson problem, in particular, the requirement of
analyticity of the initial contour for the solvability of the problem (for
the case of a sink as well as for a source) is described. The essence of
the model is the following. The movement of the contour is imitated by
the movement of a finite number of points that belong to some quasicontour.
Its movement inherits the law of the movement of the contour in
the classical sense. The existence of convex quasicontours and appropriate
position of the source-sink is proved, for which the problem
is unsolvable in the classical sense.
An obstacle for the existence of the classical
solution is the presence of points of the quasicontour where the tangent
velocity assumes the values
```$\pm\infty$ , oscillating infinitely rapidly
in the case of the source and conserving the sign in the case of a sink.
In the case of a source this determines a physically justified
movement even of a ``irregular'' initial contour,
and in the case of a sink
this clarifies the necessity of high smoothness of the initial curve.

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Last modified: April 27, 1999