English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

As one of the seven open problems in the addendum to their 1989 book"Computability in Analysis and Physics", Pour-El and Richards proposed ``...the recursion theoretic study of particular nonlinear problems of classicalimportance. Examples are the Navier-Stokes equation, the KdV equation, and thecomplex of problems associated with Feigenbaum's constant.'' In this paper, weapproach the question of whether the Navier-Stokes Equation admits recursivesolutions in the sense of Weihrauch's Type-2 Theory of Effectivity. A naturalencoding (``representation'') is constructed for the space of divergence-freevector fields on 2-dimensional open square $\Omega = (-1, 1)^2$. Thisrepresentation is shown to render first the mild solution to the StokesDirichlet problem and then a strong local solution to the nonlinearinhomogeneous incompressible Navier-Stokes initial value problem uniformlycomputable. Based on classical approaches, the proofs make use of many subtleand intricate estimates which are developed in the paper for establishing thecomputability results.

Computability of the Solutions to Navier-Stokes Equations via Recursive Approximation