The stationary Navier-Stokes equations in weighted Bessel-potential spaces

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概要

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• 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 Banachs Fixed Point Theorem.

• 社団法人 日本数学会の論文
• 2009-01-01

著者

• Schumacher Katrin

  Department Of Mathematics Technische Universitat Darmstadt

関連論文

• The stationary Navier-Stokes equations in weighted Bessel-potential spaces

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