Events for 09/22/2020 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Helena J Nussenzveig Lopes, Federal University of Rio de Janeiro

Title: Analysis of incompressible flows with helical symmetry

Abstract: 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. Regarding existence results, we will report on work in progress, joint with A. C. Bronzi and M. C. Lopes Filho.