Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | T Th 10:05am - 11:20am, at LeConte 315 |
| Office | LeConte 449 |
| Office Hours | T 11:30am - 12:30pm, or by appointment |
| Textbooks | There is no required textbook for this topic course. The material are based on the lecture notes. |
| Syllabus | Click Here |
Course Description
- This course introduces analytical methods for nonlinear partial differential equations arising in fluid dynamics. The focus is on transport-type equations and the mathematical structures underlying incompressible flows. We study the incompressible Euler equations in detail, and use them as a model to develop techniques such as energy estimates, commutator estimates, and the method of characteristics. These tools are then applied to related systems, including the surface quasi-geostrophic (SQG) equation and the primitive equations (PE), highlighting the effects of nonlocality and anisotropy.
- The course is organized into three main parts:
- Foundations: transport equations, Sobolev spaces, and analytical tools.
- Incompressible Euler equations: detailed analysis and well-posedness.
- Extensions: SQG and primitive equations.
- By the end of the course, students should be able to:
- Understand the basic structure of transport-type PDEs in fluid dynamics.
- Apply key analytical tools such as energy methods and commutator estimates.
- Analyze the incompressible Euler equations and related models.
- Recognize similarities and differences among Euler, SQG, and primitive equations.
Grades
- 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.