Two-scale convergence for thin domains and its applications to some lower-dimensional models in fluid mechanics

Inspird by similar ideas from the homogenization theory, it this paper we introduce the notion of two-scale convergence for thin domains that allow lower-dimensional approximation. We prove the compactness theorems, analogous to the one in homogenization theory. Using those results we derive lower-dimensional approximations in case of potential flow in thin pipe, the degenerated Reynolds equation for thin domain with sharp edge, and 1D approximation for power-law flow in thin pipe.

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