Asymptotic Analysis - Volume 23, issue 1

Authors: Kaidi, Nourredine | Kerdelhué, Philippe

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 23, no. 1, pp. 1-21, 2000

Authors: Marušić, Sanja | Marušić‐Paloka, Eduard

Article Type: Research Article

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.

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

Authors: Maz’ya, V.G. | Slutskii, A.S.

Article Type: Research Article

Abstract: A flow of viscous incompressible fluid in a domain &OHgr;_ϵ depending on a small parameter ϵ is considered. The domain &OHgr;_ϵ is the union of a domain &OHgr;_0 with piecewise smooth baundary and thin channels with width of order ϵ . Every channel contains one angle point of the domain &OHgr;_0 near the channel’s inlet. We prove the existence of a solution (v_ϵ,p_ϵ ) to the Navier–Stokes system such that in a neighbourhood of an angle point of the domain &OHgr;_0 the pair (v_ϵ,p_ϵ …) is equal, up to a term with finite kinetic energy, to the Jeffery–Hamel solution which describes a plane viscous source (or sink) flow between the sides of the angle. In the channels the pair (v_ϵ,p_ϵ ) asymptotically coincides with the Poiseuille solution. Asymptotic expressions for the kinetic energy and the Dirichlet integral of (v_ϵ,p_ϵ ) are obtained. Show more

Citation: Asymptotic Analysis, vol. 23, no. 1, pp. 59-89, 2000