FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**The finite points model of the Stokes--Leibenson problem for the
Hele-Shaw flow**

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 $$± ¥, 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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Location: http://mech.math.msu.su/~fpm/eng/99/991/99104h.htm

Last modified: April 27, 1999