On a class of two-dimensional flows of a dipolar incompressible fluid
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
On a temperature-dependent Hele-Shaw flow in one dimension
A model is presented for a Hele-Shaw flow with variable temperature in one space dimension. The problem to be solved is a free boundary problem for a parabolic equation with a non-linear and non-local free boundary condition. Existence and uniqueness are proved.
On bounded channel flows of viscoelastic fluids
We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can...
On fully developed flows of fluids with a pressure dependent viscosity in a pipe
Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite strong,...
On implicit constitutive theories
In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....
On internal constraints in continuum mechanics.
On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities
We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.
On second-grade fluids with vanishing viscosity.
On similarity solution of a boundary layer problem for power-law fluids
The boundary layer equations for the non-Newtonian power law fluid are examined under the classical conditions of uniform flow past a semi infinite flat plate. We investigate the behavior of the similarity solution and employing the Crocco-like transformation we establish the power series representation of the solution near the plate.
On stationary kinetic systems of Boltzmann type and their fluid limits
The first part reviews some recent ideas and L¹-existence results for non-linear stationary equations of Boltzmann type in a bounded domain in ℝⁿ and far from global Maxwellian equilibrium. That is an area not covered by the DiPerna and P. L. Lions methods for the time-dependent Boltzmann equation from the late 1980-ies. The final part discusses the more classical perturbative case close to global equilibrium and corresponding small mean free path limits of fully non-linear stationary problems....
On the behaviour of the surfaces of equilibrium in the capillary tubes when gravity goes to zero
On the blow-up set for non-Newtonian equation with a nonlinear boundary condition.
On the convergence rate of spectral approximation for the equations for nonhomogeneous asymmetric fluids
On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
On the equation of a rotating film.
On the equilibria of the extended nematic polymers under elongational flow.
On the existence of weak solutions for the initial-boundary value problem in the Jeffreys model of motion of a viscoelastic medium.
On the global existence for a regularized model of viscoelastic non-Newtonian fluid
We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like (p > 6/5), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.