MATH728 Mathematical Theory in Fluid Dynamics Spring 2023

Course Information

Instructor Dr. Changhui Tan
Lectures T Th 1:15pm - 2:30pm, at LeConte 315
Office LeConte 427
Office Hours T 10:00am - 12:00pm, or by appointment
Textbooks There is no required textbook for this topic course. The material is based on the lecture notes.
References Roman Shvydkoy, Dynamics and Analysis of Alignment Models of Collective Behavior, Springer Birkhauser, 2021.
Syllabus Click Here


Course Description

  • Collective motion is defined as the spontaneous emergence of ordered movement in a system consisting of many self-propelled agents. It can be observed in everyday life, for example in flocks of birds, schools of fish, herds of animals and also in crowds and car traffic.
  • The course will focus on the mathematical theory for models in collective dynamics. The main goal is to establish an analytical framework to study the complex nonlocal interactions, and the mathematical descriptions of collective behaviors.
  • Topics include the analysis of weak and strong solutions, local and global well-posedness, and asymptotic behaviors to a variety of models in collective dynamics, e.g. the aggregation equation, the Cucker-Smale flocking model, the Euler-alignment system, the porous medium equation.
  • Upon successful completion of this course, students will be familiar with modern analytical tools that can be used to treat with ODEs and PDEs in collective dynamics and beyond. These advanced techniques can be used to analyze a large class of time-dependent PDEs.



  • The grade will be based on class participation, occasional homework assignments, and a possible final project.


Contact Information

  • Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.