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Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...
We formulate sufficient conditions for regularity up to the boundary of a weak solution v in a subdomain Ω × (t₁,t₂) of the time-space cylinder Ω × (0,T) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that Ω is a cube.
This paper is devoted to Eulerian models for incompressible fluid-structure systems. These models are primarily derived for computational purposes as they allow to simulate in a rather straightforward way complex 3D systems. We first analyze the level set model of immersed membranes proposed in [Cottet and Maitre, Math. Models Methods Appl. Sci.16 (2006) 415–438]. We in particular show that this model can be interpreted as a generalization of so-called Korteweg fluids. We then extend this model...
In this paper we present a theory describing the diffusion limited evaporation of sessile
water droplets in presence of contact angle hysteresis. Theory describes two stages of
evaporation process: (I) evaporation with a constant radius of the droplet base; and (II)
evaporation with constant contact angle. During stage (I) the contact angle decreases from
static advancing contact angle to static receding contact angle, during stage (II) the
contact...
We study the well-posedness of an unsteady fluid-structure interaction problem.
We consider a viscous incompressible flow, which is modelled by the
Navier-Stokes equations. The structure is a collection of rigid moving bodies. The fluid
domain depends on time and is defined by the position of the structure, itself resulting
from a stress distribution coming from the fluid. The problem is then
nonlinear and the equations we deal with are coupled. We prove its local
solvability in time through two...
Dans cet article on s’intéresse à l’existence et l’unicité globale de solutions pour le système de Navier-Stokes à densité variable, lorsque la donnée initiale de la vitesse est dans l’espace de Besov homogène de régularité critique . Notons que ce résultat fait suite aux résultats de H. Abidi qui a généralisé le travail de R. Danchin. Toutefois, dans les travaux antérieurs, l’existence de la solution est obtenue pour et l’unicité est démontrée sous l’hypothèse plus restrictive Notre résultat...
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
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