Non-Stationary Stokes Flows Under Leak Boundary Conditions of Friction Type

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 $L^2$-strong solution) of this initial 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.