798 research outputs found
Existence of weak solutions up to collision for viscous fluid-solid systems with slip
We study in this paper the movement of a rigid solid inside an incompressible
Navier-Stokes flow, within a bounded domain. We consider the case where slip is
allowed at the fluid/solid interface, through a Navier condition. Taking into
account slip at the interface is very natural within this model, as classical
no-slip conditions lead to unrealistic collisional behavior between the solid
and the domain boundary. We prove for this model existence of weak solutions of
Leray type, up to collision, in three dimensions. The key point is that, due to
the slip condition, the velocity field is discontinuous across the fluid/solid
interface. This prevents from obtaining global H1 bounds on the velocity, which
makes many aspects of the theory of weak solutions for Dirichlet conditions
unadapted.Comment: 45 page
The Two Dimensional Euler Equations on Singular Exterior Domains
This paper is a follow-up of article [Gerard-Varet and Lacave, ARMA 2013], on
the existence of global weak solutions to the two dimensional Euler equations
in singular domains. In [Gerard-Varet and Lacave, ARMA 2013], we have
established the existence of weak solutions for a large class of bounded
domains, with initial vorticity in (). For unbounded domains, we
have proved a similar result only when the initial vorticity is in
() and when the domain is the exterior of a single obstacle. The goal here
is to retrieve these two restrictions: we consider general initial vorticity in
(), outside an arbitrary number of obstacles (not reduced to
points)
Computation of the drag force on a rough sphere close to a wall
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 this way, we recover and clarify the various expressions that can be found
in the litterature
Effective boundary condition at a rough surface starting from a slip condition
We consider the homogenization of the Navier-Stokes equation, set in a
channel with a rough boundary, of small amplitude and wavelength . It
was shown recently that, for any non-degenerate roughness pattern, and for any
reasonable condition imposed at the rough boundary, the homogenized boundary
condition in the limit is always no-slip. We give in this paper
error estimates for this homogenized no-slip condition, and provide a more
accurate effective boundary condition, of Navier type. Our result extends those
obtained in previous works, in which the special case of a Dirichlet condition
at the rough boundary was examined
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