Related papers: Mathematical existence results for the Doi-Edwards…
In this paper we mainly investigate the Cauchy problem of the Doi-Edwards polymer model with dimension $d\geq2$. The model was derived in the late 1970s to describe the dynamics of polymers in melts. The system contain a Navier-Stokes…
This paper establishes the existence of smooth solutions for the Doi-Edwards rheological model of viscoelastic polymer fluids in shear flows. The problem turns out to be formally equivalent to a K-BKZ equation but with constitutive…
The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic…
We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness the Doi model for large data, and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the…
We present a self-consistent method for deriving moment equations for kinetic models of polymer dynamics. The Doi model [M. Doi, J.Polymer. Sci., Polym. Phys. Ed. 19, 229 (1981)] of liquid-crystalline polymers with the Onsager…
We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation…
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and…
A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were obtained in the past one hundred years,…
In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…
We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…
We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The…
The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
In 1975 Doi and Edwards predicted that entangled polymer melts and solutions can have a constitutive instability, signified by a decreasing stress for shear rates greater than the inverse of the reptation time. Experiments did not support…
In my PhD thesis I show the existence of global-in-time weak solutions for a Navier-Stokes fluid interacting with a linearly elastic shell of Koiter type. This is achieved by the introduction of a new method for showing the compactness of…
In this paper we first employ the energetic variational method to derive a micro-macro model for compressible polymeric fluids. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
We study dynamics of a coupled system consisting of the 3D Navier--Stokes equations which is linearized near a certain Poiseuille type flow in an (unbounded) domain and a classical (possibly nonlinear) elastic plate equation for transversal…