Spectral approximation of Takens-Bogdanov point of the Navier-Stokes equations for the flow between two concentric rotating spheres

The paper studies a spectral Galerkin approximation problem of Takens-Bogdanov point of the Navier-Stokes equations for the flow between two concentric rotating spheres. The author constructs the extended system and its spectral Galerkin approximate system of Takens-Bogdanov point for the Navier-Stokes equations, and prove the regularity of solution of the extended system; the existence and the convergence of solutions of the spectral Galerkin approximate system are discussed. The spectral Galerkin approximation of Takens-Bogdanov point of the Navier-Stokes equations in two concentric rotating spheres is given, and the error estimates is presented. (c) 2006 Elsevier Inc. All rights reserved.