Joint USYD-UNSW Seminar on Stochastic PDEs: Marius Tucsnak -- Enhanced dissipation of passive scalars: a control theoretical approach

Zoom link: https://unsw.zoom.us/j/87938114945?from=addon Meeting ID: 87938114945
Password (if required): 859718 

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.