A variational approach to the theory of temperature boundary layer.
A variational principle for the nonstationary linear Navier-Stokes equations.
A Variational Principle For The Theory Of Laminar Boundary Layers In Incompressible Fluids
A variational principle for the theory of laminar boundary layers in incompressible fluids.
A vectorizable simulation method for the Boltzmann equation
A viscoelastic model with non-local damping application to the human lungs
In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...
A waiting time phenomenon for thin film equations
A wavelet Galerkin finite-element method for the biot wave equation in the fluid-saturated porous medium.
A wavelet interpolation Galerkin method for the simulation of MEMS devices under the effect of squeeze film damping.
A well-balanced finite volume scheme for 1D hemodynamic simulations*
We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q = 0. This numerical method is tested on analytical tests.
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div, where may have singularities in the domaind of definition. We study the case when is a half-plane and possesses high Fourier components, analyzing the changes brought about by the singularity . We show that absorptions of energy takes...
A zoology of boundary layers.
In meteorology and magnetohydrodynamics many different boundary layers appear. Some of them are already mathematically well known, like Ekman or Hartmann layers. Others remain unstudied, and can be much more complex. The aim of this paper is to give a simple and unified presentation of the main boundary layers, and to propose a simple method to derive their sizes and equations.
About a family of distributional products important in the applications
About a Variant of the Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation"
This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.
About an initial-boundary value problem from magneto-hydronamics.
About global existence and asymptotic behavior for two dimensional gravity water waves
The main result of this talk is a global existence theorem for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds.The proof is based on a bootstrap argument involving and estimates. The bounds are proved in the paper [5]. They rely on a normal forms paradifferential method allowing one to obtain energy estimates on the Eulerian formulation...
About estimates for the spatially homogeneous Boltzmann equation
About porosity parameters with the application of general similarity method to the case of a dissociated gas flow in the boundary layer
About steady transport equation I – -approach in domains with smooth boundaries
We investigate the steady transport equation in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields , as possible (conserving the requirement of...
About steady transport equation. II: Schauder estimates in domains with smooth boundaries.