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We analyze in classical L q (R n )-spaces, n = 2 or n = 3, 1 < q < ∞, a singular integral operator arising from the linearization of a hydrodynamical problem with a rotating obstacle. The corresponding system of partial differential equations of second order involves an angular derivative which is not subordinate to the Laplacian. The main tools are LittlewoodPaley theory and a decomposition of the singular kernel in Fourier space.

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We establish the existence, uniqueness and L q estimates of weak solutions to the stationary Stokes equations with rotation effect both in the whole space and in exterior domains. The equation arises from the study of viscous incompressible flows around a body that is rotating with a constant angular velocity, and it involves an important drift operator with unbounded variable coefficient that causes some difficulties.