Existence of global weak solutions to some regularized kinetic models for dilute polymers

Published versio

Finite-element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation

Accepted versio

An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

Published versio

Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier–Stokes system in a bounded domain Ω in Rd, d = 2 or 3, for the density ρ, the velocity u∼ and the pressure p of the fluid, with an equation of state of the form p(ρ) = cpρ γ, where cp is a positive constant and γ > 3 2 . The right-hand side of the Navier–Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. The elastic extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker–Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass diffusion term

A mixed formulation of the Monge-Kantorovich equations

Published versio

Partial L-1 Monge-Kantorovich problem: variational formulation and numerical approximation

Published versio