On Bloch Waves for the Stokes Equations
نویسندگان
چکیده
In this work, we study the Bloch wave decomposition for the Stokes equations in a periodic media in Rd. We prove that, because of the incompressibility constraint, the Bloch eigenvalues, as functions of the Bloch frequency ξ, are not continuous at the origin. Nevertheless, when ξ goes to zero in a fixed direction, we exhibit a new limit spectral problem for which the eigenvalues are directionally differentiable. Finally, we present an analogous study for the Bloch wave decomposition for a periodic perforated domain.
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