TY - JOUR
T1 - Non-Stationary Stokes Flows Under Leak Boundary Conditions of Friction Type
AU - Hiroshi Fujita
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 8
PY - 2001
DA - 2001/02
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8951.html
KW - Stokes equation, Leak boundary condition, Nonlinear semigroup.
AB - <p style="text-align: justify;">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.</p>