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.