Loading [MathJax]/extensions/MathZoom.js
Displaying 321 –
340 of
787
We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent...
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some results on...
This article deals with the low Mach number limit of the compressible Euler-Korteweg equations. It is justified rigorously that solutions of the compressible Euler-Korteweg equations converge to those of the incompressible Euler equations as the Mach number tends to zero. Furthermore, the desired convergence rates are also obtained.
The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [1, 2], after suitable para-linearizations, the system can be arranged into...
Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin...
In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...
By using the Galerkin method, we prove the existence of weak solutions for the equations of the magneto-micropolar fluid motion in two and three dimensions in space. In the two-dimensional case, we also prove that such weak solution is unique. We also prove the reproductive property.
We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a CouetteTaylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as goes to infinity. This explains rigorously some experiments.
We consider a 2D mathematical model describing the motion of a
solution of surfactants submitted to a high shear stress in a
Couette-Taylor system. We are interested in a stabilization process
obtained thanks to the shear. We prove that, if the shear stress is
large enough, there exists global in time solution for small
initial data and that the solution
of the linearized system (controlled by a nonconstant parameter) tends
to 0 as t goes to infinity. This
explains rigorously some experiments.
...
In this article, we wish to investigate the behavior of a two-layer turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects...
In this article, we wish to investigate the behavior of a two-layer k - ε
turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations.
First, we explain the difficulties inherent in the
model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent
viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical...
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal -regularity of the periodic Laplace and Stokes operators and a local-in-time existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group to obtain an -bound for the...
The evolution of a force-free granular gas with a constant restitution coefficient is
studied by means of granular hydrodynamics. We numerically solve the hydrodynamic
equations and analyze the mechanisms of cluster formation. According to our findings, the
presently accepted mode-enslaving mechanism may not be responsible for the latter
phenomenon. On the contrary, we observe that the cluster formation is mainly driven by
shock-waves, which spontaneously...
Currently displaying 321 –
340 of
787