MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Maximum principle and gradient estimates for stationary solutions of the Navier-Stokes equations; a computer aided investigation

Robert Finn, Abderrahim Ouazzi and Stefan Turek


We calculate numerically the solutions of the stationary Navier-Stokes equations in two dimensions, for a square domain with particular choices of boundary data. The data are chosen to test whether bounded disturbances on the boundary can be expected to spread into the interior of the domain. The results indicate that such behavior indeed can occur, but suggest an estimate of general form for the magnitudes of the solution and of its derivatives, analogous to classical bounds for harmonic functions.

The qualitative behavior of the solutions we found displayed some striking and unexpected features. As a corollary of the study, we obtain two new examples of non-uniqueness for stationary solutions at large Reynolds numbers.


Related publications

2010 Repository Open Access
Robert Finn, Abderrahim Quazzi and Stefan Turek

Maximum principle and gradient estimates for stationary solutions of the Navier-Stokes equations : a partly numerical investigation

In: Advances in mathematical fluid mechanics : dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday / Rolf Rannacher... (eds.)
Berlin [u. a.] : Springer, 2010. - pp. 253-269