Homogenization with an oscillating drift: from L-2-bounded to unbounded drifts, 2D compactness results, and 3D nonlocal effects
Résumé
This paper extends results obtained by Tartar (1977, 1986) and revisited in Briane and G,rard (Ann Scuola Norm Sup Pisa, to appear), on the homogenization of a Stokes equation perturbed by an oscillating drift. First, a N-dimensional scalar equation, for N a parts per thousand yen 3, and a tridimensional Stokes equation are considered in the periodic framework only assuming the L (2)-boundedness of the drift and so relaxing the equi-integrability condition of Briane and G,rard (Ann Scuola Norm Sup Pisa, to appear). Then, it is proved that the L (2)-boundedness can be removed in dimension two, provided that the divergence of the drift has a sign. On the contrary, nonlocal effects are derived in dimension three with a free divergence drift that is only bounded in L (1).