SIMON , Jacques

The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall covered by microscopic asperities because, due to the viscous dissipation, the surface irregularities bring to rest the fluid particles in contact with the wall. In mathematical terms, this corresponds to an asymptotic property...

The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall covered by microscopic asperities because, due to the viscous dissipation, the surface irregularities bring to rest the fluid particles in contact with the wall. In mathematical terms, this corresponds to an asymptotic property...

Recordamos resultados y presentamos problemas abiertos acerca de la influencia del perfil y la rugosidad de un cuerpo sólido sobre su resistencia al arrastre hidrodinámico. Mostramos además que, asintóticamente, un fluido no puede deslizarse sobre una pared recubierta de asperezas minúsculas si éstas son demasiado numerosas: en tal caso, se...

We prove, on one hand, that for a convenient body force with values in the distribution space (H−1(D))d, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier-Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual...

We study the effect of the rugosity of a wall on the solution of the Stokes system complemented with Fourier boundary conditions. We consider the case of small periodic asperities of size ". We prove that the velocity field, pressure and drag respectively converge to the velocity field, pressure and drag of a homogenized Stokes problem, where a...

This paper is concerned with the computation of the drag T associated with a body traveling at uniform velocity in a fluid governed by the stationary Navier–Stokes equations. It is assumed that the fluid fills a domain of the form Ω+u, where Ω ⊂ R3 is a reference domain and u is a displacement field. We assume only that Ω is a Lipschitz domain...

On étudie l'effet de la rugosité d'une paroi sur l'écoulement d'un fluide gouverné par les équations de Stokes avec des conditions aux limites de Fourier. On calcule l'écoulement limite et on donne des estimations, en fonction de la taille ε des aspérités, de l'écart entre la vitesse, la pression et la traı̂née et leurs limites. Dans le cas...