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

Article type: Research Article

Authors: Marušić, Sanja | Marušić‐Paloka, Eduard^;

Affiliations: Faculty of Traffic Engineering, University of Zagreb, Vukelićeva 4, 10000 Zagreb, Croatia | Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Note: [] Corresponding author.

Abstract: Inspired by the similar ideas from the homogenization theory, in this paper we introduce the notion of two‐scale convergence for thin domains that allow lower‐dimensional approximations. We prove the compactness theorem, analogous to the one in homogenization theory. Using those results we derive the lower‐dimensional models for potential flow in thin (possibly degenerated) pipe, the degenerated Reynold’s equation for viscous flow in degenerated thin domain and the 1‐dimensional approximation for the non‐Newtonian (power‐law) flow in a thin pipe.

Journal: Asymptotic Analysis, vol. 23, no. 1, pp. 23-57, 2000