A drift homogenization problem revisited (Q2883318)

The authors deal with a homogenization problem, studied by Luc Tartar, related to the Stokes equation in a bounded domain \(\Omega\) of \(\mathbb R\), perturbed by an oscillating drift term (related to the Coriolis force). The Tartar approach is based on the oscillations test functions and gives an extra zero-order term in the limit equation. When the drift is only assumed to be equi-integrable, the same limit behaviour is obtained, but the use of the direct Tartar's method is not simple. The authors propose a new method in the contest of the homogenization theory. It is based on a parametrix of the Laplace operator which permits to write the solution of the equation as a solution of a fixed point problem, and to use truncated functions even in the vector-valued case. Eventually two counter-examples are given, which provide different homogenized zero-order-terms and show the sharpness of the equi-integrability assumption.