On Computability of Navier-Stokes’ Equation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)

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 \(L_q\) 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 \(q=2\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Virginia TechBlacksburgUSA
  2. 2.University of CincinnatiCincinnatiUSA
  3. 3.TU DarmstadtDarmstadtGermany

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