The Formulation of the Navier-Stokes Equations on Riemannian Manifolds

Explore the formulation of the Navier-Stokes equations on Riemannian manifolds in this one-hour conference talk presented by Magdalena Czubak from the University of Colorado Boulder. Delivered as part of the Workshop on Geometry and Analysis of Fluid Flows with a Special Tribute to David Ebin in January 2023, the talk delves into the groundbreaking work of David Ebin and Jerrold Marsden from their 1970 seminal article. Discover the challenges and complexities arising from multiple inequivalent formulations of the Navier-Stokes equations on Riemannian manifolds, stemming from various possibilities for the Laplacian operator acting on vector fields. Examine the specific operator proposed by Ebin and Marsden for this geometric setting, and gain insights into recent developments in the study of Navier-Stokes equations within the context of Riemannian manifolds. This presentation offers a deep dive into an important topic in mathematical physics, combining elements of differential geometry, fluid dynamics, and partial differential equations.