Steady States of Fokker-planck Equations: Ii. Non-existence

Steady States of Fokker-planck Equations: I. Existence

This is the first paper in a series concerning the study of steady states of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, by using the level set method especially the integral identity which we introduced in [24], we obtain several new existence results of steady states, including stationary solutions and meas...

Steady States of Fokker-planck Equations: Iii. Degenerate Diffusion

This is the third paper in a series concerning the study of steady states of a Fokker-Planck equation in a general domain in R with Lp̄loc drift term and W 1,p̄ loc diffusion term for any p̄ > n. In this paper, we give some existence results of stationary measures of the Fokker-Planck equation under Lyapunov conditions which allow the degeneracy of diffusion.

Refined Long-time Asymptotics for Some Polymeric Fluid Flow Models

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of stationary states and the convergence towards t...

Stability of steady states in kinetic Fokker-Planck equations for Bosons and Fermions

We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and FermiDirac statistics, respectively. We establish the existence of classical solutions in the perturbative regime and prove exponential convergence towards the equilibrium. Version: November 6th, 2006

Iterative methods for solving non linear Fokker-Planck equation