Weak L2-solutions to a Stokes-like system of fourth order in bounded Lipschitz domains

We study the weak L2-solutions of the Dirichlet problem for a Stokes-like system of fourth order in a bounded Lipschitz domain G < subset of> n (n epsilon 2). For this purpose we study the operator [image omitted] (where [image omitted]) and its adjoint. Further we determine a subspace [image omitted] such that div has there a continuous inverse. This induces an orthogonal decomposition of [image omitted]. Then existence, uniqueness and a priori estimates of solutions to the system under consideration are easy consequences. With the help of the Dirichlet problem for 3 we construct a refined decomposition of M2(G).