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Dense Granular Poiseuille Flow

E. Khain (2011)

Mathematical Modelling of Natural Phenomena

We consider a dense granular shear flow in a two-dimensional system. Granular systems (composed of a large number of macroscopic particles) are far from equilibrium due to inelastic collisions between particles: an external driving is needed to maintain the motion of particles. Theoretical description of driven granular media is especially challenging for dense granular flows. This paper focuses on a gravity-driven dense granular Poiseuille flow...

Density-dependent incompressible fluids with non-Newtonian viscosity

F. Guillén-González (2004)

Czechoslovak Mathematical Journal

We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of p -coercivity and ( p - 1 ) -growth, for a given parameter p > 1 . The existence of Dirichlet weak solutions was obtained in [2], in the cases p 12 / 5 if d = 3 or p 2 if d = 2 , d being the dimension of the domain. In this paper, with help of some new estimates (which lead...

Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves

David Lannes (2008/2009)

Séminaire Équations aux dérivées partielles

This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed.

Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves

Cung The Anh (2009)

Annales Polonici Mathematici

We consider the propagation of internal waves at the interface between two layers of immiscrible fluids of different densities, under the rigid lid assumption, with the presence of surface tension and with uneven bottoms. We are interested in the case where the flow has a Boussinesq structure in both the upper and lower fluid domains. Following the global strategy introduced recently by Bona, Lannes and Saut [J. Math. Pures Appl. 89 (2008)], we derive an asymptotic model in this regime, namely the...

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