Abstract
Abstract We survey certain topological methods for problems in inviscid fluid dynamics in dimension three. The tools come from the topology of contact structures, or nowhere-integrable plane fields. The applications are most robust in the setting of fluids on Riemannian three-manifolds which are not necessarily Euclidean. For example, these methods can be used to construct surprising examples of inviscid flows in non-Euclidean geometries. Because of their topological basis, these methods point one toward a theory of “generic” fluids, where the geometry of the underlying domain is the genericity parameter.
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