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NON-STATIONARY STOKES FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE

Hiroshi Fujita
Journal of Computational Mathematics
Vol. 19, No. 1, MEMORY ISSUE DEDICATED TO THE 80TH BIRTHDAY OF PROFESSOR FENG KANG (JANUARY 2001), pp. 1-8
Stable URL: http://www.jstor.org/stable/43692898
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
NON-STATIONARY STOKES FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE
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Abstract

This paper is concerned with the initial value problem for non-stationary Stokes flows, under a certain non-linear boundary condition which can be called the leak boundary condition of friction type. Theoretically, our main purpose is to show the strong solvability (i.e., the unique existence of the L²—strong solution) of this initial value problem by means of the non-linear semi-group theory originated with Y. Kōmura. The method of analysis can be applied to other boundary or interface conditions of friction type. It should be noted that the result yields a sound basis of simulation methods for evolution problems involving these conditions.

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