Time:15:00-16:00, Wednesday, January 14 2026

Venue: E14-212, Yungu Campus

Speaker: Manuel Rissel, ShanghaiTech University

Title: Incompressible fluids controlled by finite-dimensional forces

Abstract: This talk concerns the problem of driving incompressible fluids from rest (or any other initial state) approximately to any prescribed target state, by using only forces that, at each time, belong to the same universal finite-dimensional function space. Universality refers to independence from data, control accuracy, control time, and Reynolds number. Agrachev and Sarychev proved that the Navier-Stokes equations and related systems posed on the torus are approximately controllable by finite-dimensional forces composed of only a few Fourier modes, thereby utilizing the presence of energy cascades arising from the nonlinearity. However, it is an open problem whether the Navier-Stokes system is approximately controllable when driven by finite-dimensional controls that are additionally localized in the physical space. I will mainly present recent progress on this question. Additionally, I will outline further results involving finite-dimensional controls, such as recent work on enhanced relaxation in controlled fluid flows.

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