Optimum regularity of Navier-Stokes solutions at time t = 0 and applications

  • R. Rautmann
Part of the Acta Mechanica book series (ACTA MECH.SUPP., volume 4)


Having in our mind the general rule from numerical mathematics: “more regular solutions allow approximations of a higher convergence rate also in stronger norms” first of all we point out the optimum regularity of a Navier-Stokes solution at its initial time. Then by means of our result we state H 2-convergence of a sequence of linearizations and of Rothe’s scheme to the Navier-Stokes initial-boundary value problem. By a numerical realization of this general approach, W. Borchers and our Paderborn group have calculated 3-dimensional viscous incompressible flows past a sphere (without symmetry assumptions) at Reynolds numbers 20000 [5].


Reynolds Number Stokes Operator Optimum Regularity Viscous Incompressible Flow Single Time Step 
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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • R. Rautmann
    • 1
  1. 1.Fachbereich Mathematik—InformatikUniversität GHS PaderbornPaderbornFederal Republic of Germany

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