Applied Maths Seminar: Tucsnak -- Enhanced dissipation of passive scalars: a control theoretical approach

Marius Tucsnak (University of Bordeaux) is currently visiting us, and will give a
seminar on Thursday, 22 October at 12pm in the Access Grid Room (note unusual day and
location).  

Title: Enhanced dissipation of passive scalars: a control theoretical approach 

Abstract: We propose a PDE-controllability based approach to the enhancement of
diffusive mixing for passive scalar fields.  Unlike in the existing literature, our
relaxation enhancing fields are not prescribed ab initio at every time and at every
point of the spatial domain.  Instead, we prove that time-dependent relaxation enhancing
vector fields can be obtained as state trajectories of control systems described by the
incompressible Euler equations either driven by finite-dimensional controls or by
controls localized in space.  The main ingredient of our proof is a new approximate
controllability theorem for the incompressible Euler equations on the torus.  Another
essential tool in our analysis is the exact controllability of the incompressible Euler
system driven by spatially localized forces.  

Bio: Marius Tucsnak obtained his PhD in 1992 in Orléans and his HDR in 1995 in Paris
6.  After positions in Versailles and Nancy, where he became full professor in 1997 and
directed the Elie Cartan Institute (2009--2015), he joined the University of Bordeaux
in 2015.  He has been a senior member of the IUF since 2013.  His work focuses on
control of PDEs and fluid-structure systems.  He has co-authored a monograph with George
Weiss, was an invited speaker at the 2022 ICM, and received the 2025 SIAM Reid Prize.