We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the extension of results to the case of exterior domains we use a localization procedure.
"Anisotropic -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body." J. Math. Soc. Japan 62 (1) 239 - 268, January, 2010. https://doi.org/10.2969/jmsj/06210239