Francisco Javier Suárez-Grau

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.

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

Analysis of the thin film flow in a rough domain filled with micropolar fluid

\Omega_\varepsilon

On the Navier boundary condition for viscous fluids in rough domains

of thickness

Effects of small boundary perturbation on the MHD duct flow

\varepsilon

Asymptotic Behavior of a Viscous Fluid Near a Rough Boundary

satisfying the Navier boundary condition on a periodic rough set

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

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

A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary

of period

Effects of rough boundary on the heat transfer in a thin-film flow

r_\varepsilon

On the influence of wavy riblets on the slip behaviour of viscous fluids

and amplitude