Asymptotic Behavior of a Bingham Flow in Thin Domains with Rough Boundary

Asymptotic Analysis of a Micropolar Fluid Flow in Thin Domain with a Free and Rough Boundary

Abstract. Motivated by lubrication problems, we consider a micropolar fluid flow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < ε << 1. We prove the existence and uniqueness of a solution of this problem for any value of ε and we establish some a priori estimates. Then we use the two-scale convergence technique to derive the l...

Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ϵ and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ=ϵ/μ, three different flow regimes are obtained in the limit as both of them tend to...

Asymptotic Analysis of a Micropolar Fluid Flow in a Thin Domain with a Free and Rough Boundary

On the Asymptotic Behavior of Elliptic Problems in Periodically Perforated Domains with Mixed-type Boundary Conditions

Using the periodic unfolding method, we analyze the asymptotic behavior of a class of elliptic equations with highly oscillating coefficients, in a perforated periodic domain. We consider, in each period, two types of holes and we impose, on their boundaries, different conditions of Neumann and/or Signorini types. The limit problems contain additional terms which capture both the influence of t...

Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in C, n > 1, with Lipschitz boundary, but it holds for domains in C1 with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergma...