Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
The stationary Navier-Stokes equations in weighted Bessel-potential spaces
Katrin Schumacher
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2009 Volume 61 Issue 1 Pages 1-38

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Abstract
We investigate the stationary Navier-Stokes equations in Bessel-potential spaces with Muckenhoupt weights. Since in this setting it is possible that the solutions do not posses any weak derivatives, we use the notation of very weak solutions introduced by Amann [1]. The basic tool is complex interpolation, thus we give 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 for small data by means of Banach's Fixed Point Theorem.
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© 2009 The Mathematical Society of Japan
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