A SOLUTION OF THE THREE DIMENSIONAL NAVIER STOKES EQUATIONS

Solution of the coupled Navier - Stokes equations

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract In this paper the incompressible Navier-Stokes equations are discretized by the nite element method. After linearization large, sparse systems of linear equations have to be solved. A well known problem is the occurrence of zero elements on the main diagonal. We describe ordering techniques of t...

Approximate controllability of three-dimensional Navier–Stokes equations

The paper is devoted to studying the problem of controllability for 3D Navier–Stokes equations in a bounded domain. We develop the method introduced by Agrachev and Sarychev in the 2D case and establish a sufficient condition under which the problem in question is approximately controllable by a finite-dimensional force. In the particular case of a torus, it is shown that our sufficient conditi...

Solutions to Three-dimensional Navier-stokes Equations for Incompressible Fluids

This article gives explicit solutions to the space-periodic NavierStokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations fo...

Exact controllability in projections for three-dimensional Navier–Stokes equations

The paper is devoted to studying controllability properties for 3D Navier–Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional projection. Our sufficient condition is verified for any torus in R. The proofs are based on a development of a general approach introduced by Agrachev and Saryche...

Solution of Steady Three-Dimensional Compressible Euler and Navier-Stokes Equations by an Implicit LU Scheme