Date/Time
Date(s) - 23/03/2026
11:30 am - 12:30 pm

Speaker: Roman Shvydkoy (University of Illinois at Chicago)

Location: Hamilton Hall, Room 312

Title: On regularity and asymptotics of kinetic alignment models. 

Abstract: In this talk we discuss wellposedness, regularization, and relaxation for a broad class of Fokker-Planck-Alignment models which appear in collective dynamics and many other applications. The main feature of these results, as opposed to previously known ones, is the lack of smoothness or no-vacuum requirements on the initial data. With a particular application to the classical kinetic Cucker-Smale model, we demonstrate that any bounded data with finite energy, $(1+ |v|^q) f_0 \in L^1$, $f_0 \in L^\infty$, $q \gg 2$, gives rise to a global instantly smooth solution, satisfying entropy equality and relaxing exponentially fast. The proof is based on hypocoercivity techniques and DiPerna-Lions renormalization.