Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data

Abstract

We investigate several aspects of very weak solutions u to stationary and nonstationary Navier-Stokes equations in a bounded domain Ω \( \subseteq \) ℝ3. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data u|ϕΩ = g leading to a new and very large solution class. Here we are mainly interested to investigate the ‘largest possible’ class for the more general problem with arbitrary divergence k = div u, boundary data g = u|ϕΩ. and an external force f, as weak as possible. In principle, we will follow Amann’s approach.