Some application of the implicit function theorem to the stationary Navier-Stokes equations

Volume 54 / 1991

Konstanty Holly Annales Polonici Mathematici 54 (1991), 93-109 DOI: 10.4064/ap-54-2-93-109


We prove that - in the case of typical external forces - the set of stationary solutions of the Navier-Stokes equations is the limit of the (full) sequence of sets of solutions of the appropriate Galerkin equations, in the sense of the Hausdorff metric (for every inner approximation of the space of velocities). Then the uniqueness of the N-S equations is equivalent to the uniqueness of almost every of these Galerkin equations.


  • Konstanty Holly

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