Global well-posedness for the microscopic fene model with a sharp boundary condition

TL;DR: In this article, a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) timescale of the macroscopic function of interest is presented.

TL;DR: This paper proposes an entropy satisfying conservative method to solve the Fokker–Planck equation of the finitely extensible nonlinear elastic dumbbell model for polymers, subject to homogeneous fluids.

TL;DR: In this article, the authors established the local well-posedness for the FENE dumbbell model under a class of Dirichlet-type boundary conditions dictated by the parameter $b, and showed that the probability density governed by the Fokker-Planck equation approaches zero near boundary.

TL;DR: This work establishes a local well-posedness for the full coupled FENE dumbbell model under a class of Dirichlet-type boundary conditions dictated by the parameter b, which identifies a sharp boundary requirement for the underlying density distribution.

TL;DR: In this article, a spectral Galerkin method was proposed for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers, where a smooth convex potential U that is equal to + ∞ along the boundary ∂D of the computational domain D was removed at the expense of introducing a degeneracy, through M, in the principal part of the operator.

TL;DR: In this article, the authors studied the existence of weak solutions to a coupled microscopic-macroscopic bead-spring model which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains.

TL;DR: The existence of global-in-time weak solutions to the model for a general class of spring-force-potentials including, in particular, the widely used finitely extensible nonlinear elastic (FENE) potential is established.

TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.