4 research outputs found
Hydrodynamic limit of multiscale viscoelastic models for rigid particle suspensions
We study the multiscale viscoelastic Doi model for suspensions of Brownian
rigid rod-like particles, as well as its generalization by Saintillan and
Shelley for self-propelled particles. We consider the regime of a small
Weissenberg number, which corresponds to a fast rotational diffusion compared
to the fluid velocity gradient, and we analyze the resulting hydrodynamic
approximation. More precisely, we show the asymptotic validity of macroscopic
nonlinear viscoelastic models, in form of so-called ordered fluid models, as an
expansion in the Weissenberg number. The result holds for zero Reynolds number
in 3D and for arbitrary Reynolds number in 2D. Along the way, we establish
several new well-posedness and regularity results for nonlinear fluid models,
which may be of independent interest.Comment: 64 page
Decay and absorption for the Vlasov-Navier-Stokes system with gravity in a half-space
This paper is devoted to the large time behavior of weak solutions to the three-dimensional Vlasov-Navier-Stokes system set on the half-space, with an external gravity force. This fluid-kinetic coupling arises in the modeling of sedimentation phenomena. We prove that the local density of the particles and the fluid velocity enjoy a convergence to 0 in large time and at a polynomial rate. In order to overcome the effect of the gravity, we rely on a fine analysis of the absorption phenomenon at the boundary. We obtain a family of decay estimates for the moments of the kinetic distribution, provided that the initial distribution function has a sufficient decay in the phase space
On well-posedness for thick spray equations
In this paper, we prove the local in time well-posedness of thick spray equations in Sobolev spaces, for initial data satisfying a Penrose-type stability condition. This system is a coupling between particles described by a kinetic equation and a surrounding fluid governed by compressible Navier-Stokes equations. In the thick spray regime, the volume fraction of the dispersed phase is not negligible compared to that of the fluid. We identify a suitable stability condition bearing on the initial conditions that provides estimates without loss, ensuring that the system is well-posed. It coincides with a Penrose condition appearing in earlier works on singular Vlasov equations. We also rely on crucial new estimates for averaging operators. Our approach allows to treat many variants of the model, such as collisions in the kinetic equation, non-barotropic fluid or density-dependent drag force
Concentration versus absorption for the Vlasov-Navier-Stokes system on bounded domains
International audienceWe study the large time behavior of small data solutions to the Vlasov-Navier-Stokes system set on , for a smooth bounded domain of , with homogeneous Dirichlet boundary condition for the fluid and absorption boundary condition for the kinetic phase. We prove that the fluid velocity homogenizes to while the distribution function concentrates towards a Dirac mass in velocity centered at , with an exponential rate. The proof, which follows the methods introduced in \cite{HKMM}, requires a careful analysis of the boundary effects. We also exhibit examples of classes of initial data leading to a variety of asymptotic behaviors for the kinetic density, from total absorption to no absorption at all