New Temperature Dependent Configurational Probability Diffusion Equation for Diluted FENE Polymer Fluids: Existence of Solution Results

The steady state configurational distribution diffusion equation of the standard FENE dumbbell polymer model: existence and uniqueness of solutions for arbitrary velocity gradients

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker-Planck-Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from [1], where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurat...

Local Existence for the FENE-Dumbbell Model of Polymeric Fluids

We study the well-posedness of a multi-scale model of polymeric fluids. The microscopic model is the kinetic theory of the finitely extensible nonlinear elastic (FENE) dumbbell model. The macroscopic model is the incompressible non-Newton fluids with polymer stress computed via the Kramers expression. The boundary condition of the FENE-type Fokker-Planck equation is proved to be unnecessary by ...

Configurational temperature profile in confined fluids. II. Molecular fluids

Existence Results for a Fractional Equation with State-Dependent Delay

In the last two decades, the theory of fractional calculus has gained importance and popularity, due to its wide range of applications in varied fields of sciences and engineering as viscoelasticity, electrochemistry of corrosion, chemical physics, optics and signal processing, and so on. The main object of this paper is to provide sufficient conditions for the existence of mild solutions for a...

Existence of solution for a micro-macro model of polymeric fluid: the FENE model