in the fixed reference system which can be written as:
Of course physicist had noticed the importance of nonlinear phenomena which appeared in the Navier-Stokes equation
of hydrodynamics and many other fields of physics.
Soltanov: On some modification Navier-Stokes equation
, Nonlinear Anal.
The professor of the mathematical analysis department of the Kyrgyz National University, Taalaibek Omurov, announced he found the solution to the Navier-Stokes Equation
For a striking recent example of such use of stochastic representations we refer to thework done on the Navier-Stokes equation
(see  and references therein).
The first exact solution of the Navier-stokes equation
was given by Stokes  which is concerned with the flow of a viscous incompressible fluid past an infinite horizontal plate oscillating in its own plane in an infinite mass of stationary fluid.
FFD, developed by Stam (1999) for computer flow visualization, can efficiently solve the Navier-Stokes equation
(Equation 1), energy equation (Equation 2), and species transport equation (Equation 3):
As an interesting result we have found that this functional form for velocities is a solution to the Navier-Stokes equation
when considering asymptotic behaviour, i.
Solutions were obtained using (1) a three-dimensional solution of the Navier-Stokes equation
using computational fluid dynamics and (2) Bernoulli's equation and a momentum balance in one dimension.
Many software programs utilize this approach, while other packages have either developed a simplified Navier-Stokes equation
, or simply use Bernoulli approximations to simulate metal flow.
The result, he says, is a navier-Stakes fluid without the hassle of solving a traditional Navier-Stokes equation
The 3D code is an in-house computer program based on a finite volume discretization of the incompressible Navier-Stokes equation
using the artificial compressibility method and the Roe flux-difference splitting with a third order limiter.