In this paper we deal with the three-dimensional Navier-Stokes system, posed in a cube. In this context, we prove a result concerning its global approximate controllability by means of boundary controls which act in some part of the boundary.

In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...

A perception experiment was carried out to determine the perceived prosodic boundary strength and the hierarchies of the perceived prosodic boundaries for spontaneous Chinese. The results indicate that perceived prosodic boundaries are highly correlated between intelligible and unintelligible (delexical) utterances, showing that the listeners may judge prosodic boundaries with no reference to s...

We propose an approach for boundary finding where the correspondence of a subset of boundary points to a model is simultaneously determined. Global shape parameters derived from the statistical variation of object boundary points in a training set are used to model the object. A Bayesian formulation, based on this prior knowledge and the edge information of the input image, is employed to find ...

In this paper we show the existence of solutions to a nonlinear singular second order ordinary differential equation, u(t) = a t u(t) + λf(t, u(t), u(t)), subject to periodic boundary conditions, where a > 0 is a given constant, λ > 0 is a parameter, and the nonlinearity f(t, x, y) satisfies the local Carathéodory conditions on [0, T ] × R × R. Here, we study the case that a well-ordered pair o...

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common convergence rates of the LOD, even if the boundary condition has a rapidly oscillating fine scale structure. We prove a corresponding a prior...

The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP). In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,R). Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can i...

Nonlinear two-dimensional Rayleigh–Bénard convection with periodic boundary conditions in the horizontal is studied for spatial periods near the 1:2 steady state mode interaction. The boundary conditions at the bottom are no-slip, and convection is driven by a fixed imposed temperature difference across the layer. Homotopic continuation is used to continue the boundary conditions at the top fro...

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipu...

In this paper we present a time fractional Fokker–Planck equation (fFPE) for radial twophase flow of liquid and gas in porous media. The fFPE of order a is solved for both twoand three-dimensional flow patterns using the Laplace transform method. The general solutions of the fFPE for both twoand threedimensional flows are given as a convolution integral of the input and a kernel in the Laplace ...