Stationary Navier—Stokes Equations

  • Alain Bensoussan
  • Jens Frehse
Part of the Applied Mathematical Sciences book series (AMS, volume 151)


We study here the regularity of solutions of the stationary Navier—Stokes equations. For the usual Navier—Stokes equations for incompressible fluids on a bounded domain, where the time variable intervenes, the issue of regularity of weak solutions is an open problem in dimension n = 3 (see J. Leray [68] or O.A. Ladyzenskaya, V.A. Solonnikov, N.N. Ural’tseva [67] for the background). Only partial regularity is available; see L. Caffarelli, R. Kohn, L. Nirenberg [9].


Weak Solution Green Function Regular Solution Pressure Equation Maximum Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alain Bensoussan
    • 1
  • Jens Frehse
    • 2
  1. 1.CNESParisFrance
  2. 2.Institut für Angewandte MathematikUniversität BonnBonnGermany

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