Lisbon Webinar in Analysis and Differential Equations

Salas 6.2.33 (Ciências ULisboa) e P3.10 (IST), com transmissão via Zoom

13h30-14h30 Europe/Lisbon (IST, room P3.10, Mathematics Building - online)

Yingfei Yi (University of Alberta)
Quasi-Stationary Distributions

Quasi-stationary distributions (QSDs) are those almost invariant to a diffusion process over exponentially long time. Representing important transient stochastic dynamics, they arise frequently in applications especially in chemical reactions and population systems admitting extinction states. This talk will present some rigorous results on the existence, uniqueness, concentration, and convergence of QSDs along with their connections to the spectra of the Fokker-Planck operators.

14h30-15h30 Europe/Lisbon (FCUL | room 6.2.33 - online)

Hyeong-Ohk Bae (Ajou University, Republic of Korea)
Interaction of particles and an incompressible fluid

We present a new coupled kinetic-fluid model for the interactions between Cucker-Smale (C-S) flocking particles and incompressible fluid on the periodic spatial domain  and in an infinite channel.

Our coupled system consists of the kinetic Cucker-Smale equation and the incompressible Navier-Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of an individual C-S particle and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast.

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.