The formulation of the Navier–Stokes equations on Riemannian manifolds

Chi-Hin Chan, Magdalena Czubak*, Marcelo M. Disconzi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider the generalization of the Navier–Stokes equation from Rn to the Riemannian manifolds. There are inequivalent formulations of the Navier–Stokes equation on manifolds due to the different possibilities for the Laplacian operator acting on vector fields on a Riemannian manifold. We present several distinct arguments that indicate that the form of the equations proposed by Ebin and Marsden in 1970 should be adopted as the correct generalization of the Navier–Stokes to the Riemannian manifolds.

Original languageEnglish
Pages (from-to)335-346
Number of pages12
JournalJournal of Geometry and Physics
StatePublished - 1 Nov 2017


  • Deformation tensor
  • Formulation
  • Navier–Stokes
  • Riemannian manifolds

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