Spontaneous periodic orbits in the Navier-Stokes flow

CDSNS Colloquium
Friday, October 21, 2022 - 3:30pm for 1 hour (actually 50 minutes)
Online via Zoom (Skiles 006 viewing party)
Maxime Brenden – Ecole Polytechnique – maxime.breden@polytechnique.eduhttps://www.polytechnique.edu/annuaire/breden-maxime
Alex Blumenthal

Please Note: Zoom link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

In this talk, I will present results concerning the existence and the precise description of periodic solutions of the Navier-Stokes equations with a time- independent forcing, obtained in collaboration with Jan Bouwe van den Berg (VU Amsterdam), Jean-Philippe Lessard (McGill) and Lennaert van Veen (Ontario TU).

These results are obtained by combining numerical simulations, a posteriori error estimates, interval arithmetic, and a fixed point theorem applied to a quasi-Newton operator, which yields the existence of an exact solution in a small and explicit neighborhood of the numerical one.

I will first introduce the main ideas and techniques required for this type of approach on a simple example, and then discuss their usage in more complex settings like the Navier-Stokes equations.