Diffusiophoresis is a phenomenon which induces a transport of microparticles suspended in a solvent when salinity gradients are present. This effect, whose origin relies on charge effects at the surface of the particles, results in a tiny velocity drift with respect to the fluid flow which advect them. In this talk, I will discuss the physical origin of diffusiophoresis and its consequences...
In this talk, I will present a justi cation of the transition from a compressible (inviscid) system with singular pressure, modeling short range repulsive forces, towards a mixed compressible-incompressible system modeling partially congested dynamics. These systems may be used for the modeling of mixtures, of collective motions or partially free surface flows where a maximal constraint on the...
The first result concerning the problem of the existence of weak solutions "à la Leray'", in dimensions 2 or 3, for the stationary Navier-Stokes system governing the flow of compressible, viscous fluids was obtained in 1998 by P-L. Lions under the hypothesis of isotropic diffusion at constant shear and volume viscosities.
In this talk I will present a new proof of this result, witch will...
We are interesting in modelling a flow with compressible bubbles by a homogeneisation method. At the microscopic scale, the fluid is described by the compressible Navier-Stokes system, while the bubbles behaviour is described individually. The novelty of the model relies in the fact that it takes into account the surface tension at the interfaces. Assuming that the number of bubbles diverges,...
Concerning geophysical or astrophysical objects, we sometimes have measurements of the heat flux that escapes from them. For instance, the net heat flux leaving the Earth is approximately $47$ TW (Davies and Davies, Solid Earth, 2010), while the luminosity (``heat flux'' in astrophysics) of the Sun is $3.83\sim10^26$ W. Given that the heat flux is transported by convection, at least partly,...
We consider a model introduced by Saintillan and Shelley to describe active suspensions of elongated particles. This model, which generalizes the classical Doi model for passive suspensions, couples a Stokes equation for the fluid substrate and a transport equation for the density distribution of particles in space and orientation. We investigate mixing properties of this model (damping and...
We consider the $\alpha$-Euler equations on a bounded domain with Dirichlet boundary conditions in dimension two. We prove the convergence to the Euler equations when $\alpha$ goes to $0$ when the potential vorticity belongs to $L^p$ with $p\geq1$ or is a bounded positive measure.
We are interested in the global existence and uniqueness issue for systems of PDEs describing the evolution of non-homogeneous viscous fluids.
In particular, we focus on the non-homogeneous incompressible Navier-Stokes system (INS) and on the system for pressureless gases (PNS). Despite their strong formal similarity -- coupling between a mass conservation equation and a parabolic-type...
We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. Taking into account these lubrication effects in numerical simulations is a difficult problem: capturing the singularity requires, for...
In this talk we explain how to prove the nonlinear asymptotic stability of multiD periodic steady solutions that are diffusively spectrally stable, focusing our attention on the 2D case. Our goal is to extend the comprehensive theory now available for plane periodic waves to the multidimensional context. All this work is performed on reaction-diffusion systems but we expect it can be extended...
In this talk we will review different recent aspects of the regularity for the 3D Navier-Stokes equations: (i) new versions of epsilon regularity, (ii) concentration near potential singularities, (iii) quantitative regularity, (iv) geometric aspects. The talk is based on works with Dallas Albritton, Tobias Barker, Pedro Fernandez-Dalgo and Jin Tan.
Although multiphase flows are ubiquitous in natural and industrial systems, the comprehension of the physical mechanisms at stake is still a challenge. In particular, the link between the processes at the microscale -- grain size, shape, asperities -- and the behavior at larger scale (particle suspension, transport, emergence of instabilities\ldots) remains unknown. Based on laboratory...
I will present a class of evolution equations which are characterized by the presence of an upper density constraint and of the gradient of an unknown, scalar, pressure affecting the drift in order to enforce such a density constraint. We studied these PDEs, in a series of papers in collaboration with Bertrand Maury and other co-authors, motivated by their applications to crowd motion models,...
