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Knotted vortex lines and vortex tubes in stationary fluid flows. (English) Zbl 1321.35182
Summary: We review recent research on certain geometric aspects of the vortex lines of stationary ideal fluids. We mainly focus on the study of knotted and linked vortex lines and vortex tubes, which is a topic that can be traced back to Lord Kelvin and was popularised by the works of Arnold and Moffatt on topological hydrodynamics in the 1960s.
In this context, we provide a leisurely introduction to some recent results concerning the existence of stationary solutions of the Euler equations in Euclidean space with a prescribed set of vortex lines and vortex tubes of arbitrarily complicated topology.

MSC:
35Q41 Time-dependent Schrödinger equations and Dirac equations
76B47 Vortex flows for incompressible inviscid fluids
76-03 History of fluid mechanics
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
01A65 Development of contemporary mathematics
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