Stochastic sigma-convergence and applications

Details Stochastic sigma-convergence and applications Stochastic sigma-convergence and applications

2011-06-02

arxiv.org/abs/1106.0409v1

Mathematics

Analysis of PDEs

49 pages

Scientific paper

Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems simultaneously, and also separately. Our approach, the stochastic sigma-convergence, can be seen either as a multiscale stochastic approach since deterministic homogenization theory can be seen as a special case of stochastic homogenization theory (see Theorem 3), or as a conjunction of the stochastic and deterministic approaches, both taken globally, but also each separately. One of the main applications of our results is the homogenization of a model of rotating fluids.

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