Regularity of solutions to some variational inequalities for the Stokes equations

摘要

The purpose of this paper is to give results on the regularity of solutions to some variational inequalities for the Stokes equations. In 1993, H. Fujita proposed new boundary conditions for the problem of the steady motion of viscous incompressible fluid. These boundary conditions, which he called the conditions of friction type, are kinds of unilateral ones. The existence and uniquenesson-uniqueness are also established by H. Fujita. In this paper, we are going to prove that the velocity aid the pressure actually belong to the H~2 and H~1 spaces, respectively. The results are expected to be of use for the analysis of related non-stationary problems and finite element approximations both for the Stokes and Navier-Stokes equations.