On the Existence and Uniqueness of an Rν-Generalized Solution to the Stokes Problem with Corner Singularity

Abstract

We consider the Stokes problem with the homogeneous Dirichlet boundary condition in a polygonal domain with one re-entrant corner on its boundary. We define an Rν-generalized solution of the problem in a nonsymmetric variational formulation. Such defined solution allows us to construct numerical methods for finding an approximate solution without loss of accuracy. In the paper, the existence and uniqueness of an Rν-generalized solution in weighted sets is proved.