The Stokes equation, arising from linearization of the Navier Stokes equations, requires to find the fluid velocity and pressure field on a domain with prescribed initial and boundary data. The main difficulty stems from the fact that the boundary data is only on part of the whole set of unknowns, e.g. the velocity, but not the pressure. A representation of the solution can be obtained in terms of one unknown, the normal derivative of the pressure at the boundary. This unknown is then determined as the solution of an integral equation obtained from the incompressibility condition of the velocity field.I will discuss the advantages of such representation together with a short overview of other alternatives.
This is based on joint work with HoeWoon Kim and Ron Guenther.