We consider finite deformations of the p+ 2-dimensional Schwarzschild geometry which obey the vacuum Einstein equation, preserve the mean curvature and induced conformal metric on a sphere a distance λ from the horizon and are regular on the future horizon. We show perturbatively that in the limit λ → 0 the deformations are given by solutions of the nonlinear incompressible Navier-Stokes equati...

We describe a method to compute veriied enclosures for solutions of the stationary Navier-Stokes equation in two-dimensional bounded domains. In order to obtain error bounds for numerical approximations , we use the theorem of Newton{Kantorovich. Therefore, we compute approximations for the stream function of the ow and upper bounds of the defect in H ?2 (); we determine an upper bound for the ...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non–local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The a...

We consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. A parallel algorithm based on a direction splitting approach is implemented. We are targeting the massively parallel computer as well as clusters of many-core nodes. The implementation is tested on the IBM Blue Gene/P supercomputer and two Linux ...

In this article, we analyze the flow of a fluid through a coupled Stokes-Darcy domain. The fluid in each domain is non-Newtonian, modeled by the generalized nonlinear Stokes equation in the free flow region and the generalized nonlinear Darcy equation in the porous medium. A flow rate is specified along the inflow portion of the free flow boundary. We show existence and uniqueness of a variatio...

We study the Stokes equation with high-contrast viscosity coefficient and this regime corresponds to a small Reynolds number regime because viscosity is inversely proportional to the Reynolds number. Numerical solution to the Stokes flow problems especially with high-contrast variations in viscosity is critically needed in the computational geodynamics community. One of the main applications of...

We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and stabilizes the linearized equation. The proof of this fact is based on a truncated observability inequality, the regularizing property for the linearized equation...

The Schur complement of a model problem is considered as a preconditioner for the Uzawa type schemes for the generalized Stokes problem (the Stokes problem with the additional term αu in the motion equation). The implementation of the preconditioned method requires for each iteration only one extra solution of the Poisson equation with Neumann boundary conditions. For a wide class of 2D and 3D ...

Here ν = 0 for the Euler equation and ν > 0 for the Navier–Stokes equation. We assume that the initial vector field, v(x, 0) = u(x), is given by a smooth, bounded, divergence–free function u(x) of finite energy. Then a smooth solution v(x, t) is known to exist in some finite time interval 0 ≤ t < T . It is an open problem, for both the Euler and the Navier–Stokes equations, if blow–up can occur...

Approximated solutions to two-dimensional and axisymmetric jet impinging flows have been presented here. Assumptions have been made to reduce the related full Navier-Stokes equations to a non-linear ordinary differential equation. The Admomian decomposition method (ADM) has been employed to obtain an approximated solution to this differential equation. A trial and error strategy has been used t...