An approximate layering method for the Navier-Stokes equations in bounded cylinders (Q801754)

The so called layering method for solving the Navier-Stokes problem is presented. The Euler equation is approximativelly solved, using initial conditions which are obtained from a Stokes problem, related with the initial problem, on successive steps in time. The aim of the paper is to prove the convergence of this solution, when time-step tends to zero, towards the solution of the initial Navier-Stokes problem. Some properties of the semigroup-operator generated by the Stokes equation are used, and an integral representation for the solution of the Navier- Stokes equations is proved. The result is compared with those of Marsden and Chorin [see e.g.: \textit{A. J. Chorin}, J. Fluid Mech. 57, 785-796 (1973)]; the present method does not need an exact solution of the Euler equation.