We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical...
We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
Our concern is the computation of optimal shapes in problems involving (−). We focus on the energy (Ω) associated to the solution
of the basic Dirichlet problem ( − )
= 1 in Ω, = 0 in Ω. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving plane...
In meteorology and magnetohydrodynamics many different boundary layers appear. Some of them are already mathematically well known, like Ekman or Hartmann layers. Others remain unstudied, and can be much more complex. The aim of this paper is to give a simple and unified presentation of the main boundary layers, and to propose a simple method to derive their sizes and equations.
These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.
L’objet de cette note est le problème de Cauchy pour l’équation de Prandtl, dans des espaces de régularité Sobolev. Nous discutons de façon synthétique des résultats récents [], établissant le caractère fortement linéairement mal posé de ce problème.
We consider the homogenization of elliptic systems with -periodic coefficients. Classical two-scale approximation yields an error inside the domain. We discuss here the existence
of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis substantially extends previous results obtained for
polygonal domains with sides of rational slopes.
We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.
In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.
In this paper, we review recent results on wall laws for viscous fluids near rough
surfaces, of small amplitude and wavelength ε. When the surface is
“genuinely rough”, the wall law at first order is the Dirichlet wall law: the fluid
satisfies a “no-slip” boundary condition on the homogenized surface. We compare the
various mathematical characterizations of genuine roughness, and the corresponding
homogenization results....
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