Manuel Luna-Laynez

ASYMPTOTIC BEHAVIOR OF A VISCOUS FLUID WITH SLIP BOUNDARY CONDITIONS ON A SLIGHTLY ROUGH WALL

For an oscillating boundary of period and amplitude e, it is known that the asymptotic behavior when e tends to zero of a three-dimensional viscous fluid satisfying slip boundary conditions is the same as if we assume no-slip (adherence) boundary conditions. Here we consider the case where the period is still e but the amplitude is δe with δe/e converging to zero. We show that if tends to infinity, the equivalence between the slip and no-slip conditions still holds. If the limit of belongs to (0, +∞) (critical size), then we still have the slip boundary conditions in the limit but with a bigger friction coefficient. In the case where tends to zero the boundary behaves as a plane boundary. Besides the limit equation, we also obtain an approximation (corrector result) of the pressure and the velocity in the strong topology of L2 and H1 respectively.

An adaptation of the multi-scale methods for the analysis of very thin reticulated structures

Abstract The purpose of this Note is to present a new approach to the analysis of thin reticulated structures involving several parameters. The method is related to the two-scale convergence method.

Asymptotic Behavior of the Navier--Stokes System in a Thin Domain with Navier Condition on a Slightly Rough Boundary

We study the asymptotic behavior of the solutions of the Navier--Stokes system in a thin domain

Numerical Approximation of a One-Dimensional Elliptic Optimal Design Problem

\Omega_\varepsilon

Optimal design problems for a non-linear cost in the gradient: numerical results

of thickness

Homogenization of the Poisson equation with Dirichlet conditions in random perforated domains

\varepsilon

On the Navier boundary condition for viscous fluids in rough domains

satisfying the Navier boundary condition on a periodic rough set

Asymptotic Behavior of a Viscous Fluid Near a Rough Boundary

\Gamma_\varepsilon\subset \partial\Omega_\varepsilon

Effect of Roughness on the Flow of a Fluid Against Periodic and Nonperiodic Rough Boundaries

of period

Discretization of Coefficient Control Problems with a Nonlinear Cost in the Gradient

r_\varepsilon