Computational & Applied Mathematics (CAM) Seminar
Student No.:30
Time:Wed 09:30-11:30
Instructor:Shi Zuoqiang, Yu Hui  
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-8-22
Ending Date:2018-8-22


Time: 09:30-10:30

Title: Local sensitivity analysis for flocking and synchronization models

Speaker: Seung-Yeal Ha [Dept. of Mathematical Sciences, Seoul National Univ.]

Abstract: In this talk, we introduce two random flocking and synchronization models, namely random Cucker-Smale model and random Kuramoto model, and then present local sensitivity analysis for those particle and kinetic models based on the uniform stability analysis and propagation of Sobolev regularity in random parameter space. This is a joint work with Shi Jin (UW-Madison) and Jinwook Jung (SNU).

Time: 10:30-11:30

Title: Interaction of particles and an incompressible fluid

Speaker: Hyeong-Ohk Bae [Dept. of Financial Engineering, Ajou Univ.]

Abstract: 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 T^d . 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 particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast. This is a joint work with Seung-Yeal Ha (SNU) and Yongsik Kim (Ajou).