There are inequivalent formulations of the Navier-Stokes equations on the Riemannian manifolds. This is due to the different possibilities for the Laplacian operator acting on vector fields. In this talk, we discuss some of the possible choices, and present a recent progress in the search for the "correct" viscosity operator in the setting of Riemannian manifolds.
The viscosity operator on the Riemannian manifolds
Magdalena Czubak, University of Colorado Boulder
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs