A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data

We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier-Stokes equations in a bounded domain Omega subset of R-3. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data leading to a very large solution class of low regularity. Here we are mainly interested in the investigation of the "largest possible" class of solutions u for the more general problem with arbitrary divergence k = div u, boundary data g = u|(partial derivative Omega) and an external force f, as weak as possible, but maintaining uniqueness. In principle, we will follow Amann's approach.