[Dottorcomp] Seminari di Matematica Applicata, 17/12/2024, Michele Coti Zelati

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 17 Dicembre 2024, alle ore 15 precise, presso la sala conferenze
dell'IMATI di Pavia,

Michele Coti Zelati (Imperial College London)

terrà un seminario dal titolo:

Wave propagation in hydrodynamic stability.

Abstract: The stability of shear flows in the fluid mechanics is an old
problem dating back to the famous Reynolds experiments in 1883. The
question is to quantify the size of the basin of attraction of equilibria
of the Navier-Stokes equations depending on the viscosity parameters,
giving rise to the so-called stability threshold. In the case of a
three-dimensional homogeneous fluid, it is known that the Couette flow has
a stability threshold proportional to the viscosity, and this is sharp in
view of a linear instability mechanism known as the lift-up effect. In this
talk, I will explain how to exploit certain physical mechanisms to improve
this bound: these can be identified with stratification (i.e.
non-homogeneity in the fluid density) or rotation (i.e. Coriolis force).
Either mechanism gives rise to oscillations which suppress the lift-effect.
This can be captured at the linear level in an explicit manner, and at the
nonlinear level by combining sharp energy estimates with suitable
dispersive estimates.