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Differential forms, fluids, and finite models. (English) Zbl 1223.58003

The Navier-Stokes equation is rewritten in terms of differential forms, giving an abstraction of it that is suitable for the expression in both a smooth Riemannian manifold and in the finite cochain complex setting. Two examples of these finite models are considered and, in the latter case, some approximation results are proved. Some useful properties of these finite models are derived.

This work consists of the following basic parts: viscous incompressible fluids; algebraic and analytic considerations; finite models.

MSC:
58A10Differential forms (global analysis)
76D05Navier-Stokes equations (fluid dynamics)
35Q30Stokes and Navier-Stokes equations