Abstract
In this paper we describe the results of numerical studies of solutions of the Navier-Stokes System (NSS) under the boundary conditions introduced recently in the paper by Dinaburg et al. (A new boundary problem for the two-dimensional Navier-Stokes system, see this issue of this journal). First, we investigate the decay of Fourier modes, confirming the results and conjectures made in Dinaburg et al. (A new boundary problem for the two-dimensional Navier-Stokes system, see this issue of this journal). Second, we explore the growth of the total energy and enstrophy, which is possible under the adopted boundary conditions. We show that the solutions of the finite-dimensional Galerkin approximations to the NSS may diverge to infinity in finite time, i.e. their energy may blow up.
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