Mathematics Colloquium

Wednesday,1  February, 2023, 5-6 pm

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Venue: Ramanujan Hall

Host: Neela Nataraj

Speaker: Jean-Pierre Raymond

Affiliation: Paul Sabatier University, Toulouse

Title: Stabilization of fluid flows using reduced order model based on spectral projections

Abstract: We will present results concerning the stabilization of fluid flows, or systems coupling fluid flow equations with convection-diffusion equations. We are interested in the local stabilization around unstable stationary solutions. We build feedback laws (in the case of total information) for reduced models defined by spectral projection. We prove, in some of the studied cases, that the feedback law defined from the reduced model also stabilizes the initial system with an exponential decay rate a priori fixed. We also establish convergence rates of feedback laws for models approximated by a Finite Element Method towards the feedback law of the original model. This approach can be used by other type of approximation. This work is in collaboration with M. Badra (IMT).

This numerical approach has been used in a series of papers with many collaborators (even if, as mentioned above, all the assumptions, ensuring convergence rates of approximate feedback laws, have not yet been proved in all these cases).