Related papers: The Feynman-Lagerstrom criterion for boundary laye…

We study the regularity criteria for weak solutions to the $3D$ incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the boundary effects. A boundary regularity theorem is proved on…

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…

Vorticity is locally created on a boundary at the rate measured by the boundary vorticity flux, which can be further decomposed as the sum of the orbital rotation and the (generalized) spin. For incompressible viscous flow interacting with…

We report an investigation of the equilibrium and dynamic properties of polyelectrolyte solutions confined between platinum surfaces with a dynamic Surface Force Apparatus. The polyelectrolyte adsorbs on the surfaces in a dense compact…

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…

The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary…

We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the…

In this paper a model for viscous boundary and shear layers in three-dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the…

This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent…

Static manifolds with boundary were recently introduced by Cruz and Vit\'orio in the context of the prescribed scalar curvature problem in a manifold with boundary with prescribed mean curvature. This kind of manifold is also interesting…

Here we build some effective boundary conditions to be used in numerical calculations in order to avoid the thin meshing usually required in problems involving Hartmann layers near a locally plane wall. Wall model are provided for both…

The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…

We derive an effective boundary condition for granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit…

Following the previous part of our study on unsteady non-New\-to\-nian fluid flows with boundary conditions of friction type we consider in this paper the case of pseudo-plastic (shear thinning) fluids. The problem is described by a…

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…

H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space $\R^3$ based on two velocity components. Recently, one of the present authors extended this result…

We have measured the stability boundary for steady electrically-driven convective flow in thin, freely suspended films of Smectic-A liquid crystal. The thinness and layered structure of the films supress two- and three-dimensional…

Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, elastic turbulence possesses a boundary layer where the…