Bloch waves for a solid-fluid mixture
Cauchy problem for the non-newtonian viscous incompressible fluid
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor , where the nonlinear function satisfies or . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for for both models. Then, under vanishing higher viscosity , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for , its uniqueness and...
Choosing Hydrodynamic Fields
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed in the context of granular fluids and multi-component fluids. In the first case, the relevance of temperature or energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature and single...
Conjugate heat transfer of mixed convection for viscoelastic fluid past a stretching sheet.
Conservation laws for incompressible fluids.
Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation
We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer et al., SIAM J. Math. Anal.33 (2002) 1033–1047], which is a special case of Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal.113 (1991) 97–120]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical...
Convexity of Capillary Surfaces in the Outer Space.
Decay of solutions to equations modelling incompressible bipolar non-Newtonian fluids.
Deduzione della teoria dei fluidi maxwelliani dalla termodinamica dei sistemi continui
Density-dependent incompressible fluids with non-Newtonian viscosity
We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of -coercivity and -growth, for a given parameter . The existence of Dirichlet weak solutions was obtained in [2], in the cases if or if , being the dimension of the domain. In this paper, with help of some new estimates (which lead...
Development of three dimensional constitutive theories based on lower dimensional experimental data
Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate...
Disclinations and hedgehogs in nematic liquid crystals with variable degree of orientation
There is enough evidence to re-examine disclinations and hedgehogs, the singularities often observed in nematic liquid crystals, in the light of a new theory that allows for local changes in the degree of orientation.
Distributed control for multistate modified Navier-Stokes equations
The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.
Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem
Dual Combined Finite Element Methods For Non-Newtonian Flow (II) Parameter-Dependent Problem
This is the second part of the paper for a Non-Newtonian flow. Dual combined Finite Element Methods are used to investigate the little parameter-dependent problem arising in a nonliner three field version of the Stokes system for incompressible fluids, where the viscosity obeys a general law including the Carreau's law and the Power law. Certain parameter-independent error bounds are obtained which solved the problem proposed by Baranger in [4] in a unifying way. We also give some stable finite...
Dynamics of granular fluids
Écoulement d'un fluide rigide visco-plastique incompressible
Effect of magnetic field on thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid.
Effects of Hall current on the pulsating flow of a third grade fluid.
Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid.