On Computability of Navier-Stokes’ Equation

Abstract

We approach the question of whether the Navier-Stokes Equation admits recursive solutions in the sense of Weihrauch’s Type-2 Theory of Effectivity: A suitable encoding (“representation”) is carefully constructed for the space of solenoidal vector fields in the Lq sense over the d-dimensional open unit cube with zero boundary condition. This is shown to render both the Helmholtz projection and the semigroup generated by the Stokes operator uniformly computable in the case q = 2.