The analysis of incompressible flows under different symmetry reductions is an ongoing topic of research. While flows with translational symmetry – 2D flows – and axisymmetric flows have a broad associated literature, helically symmetric flows have attracted less mathematical attention.

Helically symmetric flows are those invariant under simultaneous rotation and translation with respect to a fixed axis. From the point of view of mathematical analysis, flows with helical symmetry lie between 2D flows and axisymmetric flows. In this talk I will illustrate this observation with a discussion of both existence theorems and vanishing viscosity results for helically symmetric fluid flow, and I will compare these results with those for 2D and axisymmetric flows. Regarding existence results, we will report on work in progress, joint with Anne Bronzi and Milton Lopes Filho.