On regularity and asymptotics of kinetic alignment models

📅 martes 18 de noviembre — 13:00

📍 Aula A25, Facultad de Ciencias

👤Conferenciante: Roman Shvydkoy (University of Illinois at Chicago)

📖 Título: On regularity and asymptotics of kinetic alignment models

📄 Resumen: 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 regularity 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 high moment, $(1+ |v|^q) f_0 \in L^1$, $f_0 \in L^\infty$,  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.