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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...
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
In this paper, we are interested in the modelling and the finite element
approximation of a petroleum reservoir, in axisymmetric form. The flow in the
porous medium is governed by the Darcy-Forchheimer equation coupled with a
rather exhaustive energy equation. The semi-discretized problem is put under a
mixed variational formulation, whose approximation is achieved by means of
conservative Raviart-Thomas elements for the fluxes and of piecewise constant
elements for the pressure and the temperature....
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