In this talk, I will present a new hydrodynamic model for synchronization phenomena which is a type of pressureless Euler system with nonlocal interaction forces. For the proposed system, we first establish local-in-time existence and uniqueness of classical solutions. For the case of identical natural frequencies, we provide synchronization estimates under suitable assumptions on the initial configurations. We also analyze critical thresholds leading to finite-time blow-up or global-in-time existence of classical solutions. Finally, we numerically investigate synchronization, finite-time blow-up, phase transitions, and hysteresis phenomena.
-Posters will be displayed on this date.
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Posters
Dongha Kim: Spectral properties of layer potentials arising from comductivity problems in composite media
Sungwook Jang: Sarkisov Program