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UID:20250715T010545EDT-11586sUEzJ@132.216.98.100
DTSTAMP:20250715T050545Z
DESCRIPTION:Title: Verifying global stability of fluid flows despite transi
 ent growth of energy.\n\nAbstract: Verifying nonlinear stability of a lami
 nar fluid flow against all perturbations is a classic challenge in fluid d
 ynamics. All past results rely on monotonic decrease of a perturbation ene
 rgy or a similar quadratic generalized energy. This 'energy method' cannot
  show global stability of any flow in which perturbation energy may grow t
 ransiently. For the many flows that allow transient energy growth but seem
  to be globally stable (e.g. pipe flow and other parallel shear flows at c
 ertain Reynolds numbers) there has been no way to mathematically verify gl
 obal stability. After explaining why the energy method was the only way to
  verify global stability of fluid flows for over 100 years\, I will descri
 be a different approach that is broadly applicable but more technical. Thi
 s approach\, proposed in 2012 by Goulart and Chernyshenko\, uses sum-of-sq
 uares polynomials to computationally construct non-quadratic Lyapunov func
 tions that decrease monotonically for all flow perturbations. I will prese
 nt a computational implementation of this approach for the example of 2D p
 lane Couette flow\, where we have verified global stability at Reynolds nu
 mbers above the energy stability threshold. This energy stability result f
 or 2D Couette flow had not been improved upon since being found by Orr in 
 1907. The results I will present are the first verification of global stab
 ility – for any fluid flow – that surpasses the energy method. This is
  joint work with Federico Fuentes (Universidad Católica de Chile) and Ser
 gei Chernyshenko (Imperial College London).\n\nWeb site : https://dms.umon
 treal.ca/~mathapp/index_fr.html\n\nSeminar Applied Mathematics\n	Please con
 tact : damien.tageddine [at] mail.mcgill.ca\n
DTSTART:20221003T200000Z
DTEND:20221003T210000Z
SUMMARY:David Goluskin (University of Victoria)
URL:/mathstat/channels/event/david-goluskin-university
 -victoria-342425
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