The stationary Navier-Stokes equations in weightedBessel-potential spaces

摘要

We investigate the stationary Navier-Stokes equations in Bessel-potential spaces with Muckenhoupt weights. Since in this setting it is possible thatthe solutions do not posses any weak derivatives, we use the notation of very weaksolutions introduced by Amann 1. The basic tool is complex interpolation, thus wegive a characterization of the interpolation spaces of the spaces of data and solutions.Then we establish a theory of solutions to the Stokes equations in weighted Bessel-potential spaces and use this to prove solvability of the Navier-Stokes equations forsmall data by means of Banach's Fixed Point Theorem.