Helena J. Nussenzveig Lopes

Universidade Federal do Rio de Janeiro

Analysis of incompressible flows with helical symmetry

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. These flows arise in real world applications such as the flow generated by a rotating blade. From the point of view of mathematical analysis, flows with helical symmetry lie between 2D flows and axisymmetric flows. The purpose of the talk is to illustrate this observation, discussing both existence theorems and vanishing viscosity results for helically symmetric fluid flow, and establishing comparisons with 2D and axisymmetric cases.