Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | Tu Th 9:25am - 10:40am, at HBH 227 |
| Office | HBH 426 |
| Office Hours | M 2:00pm - 4:00pm, or by appointment |
| Textbooks | There are no required textbooks. |
| References | Lawrence C. Evans, Partial Differential Equations: Second Edition, Graduate Studies in Mathematics 19, 2010. (ISBN: 978-0821849743) |
| Andrew J. Majda and Andrea L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics 27, 2001. (ISBN: 978-0521639484) |
Course Description
- We aim to cover the mathematical theories for three important topics in partial differential equations. A brief outline is as follows:
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- Second order elliptic equations:
- Laplace equation.
- Sobolev spaces, embedding, interpolation.
- Weak solutions, Lax-Milgram theorem, regularity. - Second order parabolic equations:
- Heat equation.
- Weak solutions, maximum principle.
- Semi-group theory, application on the Navier-Stokes equations. - The incompressible Euler equations:
- Vorticity-stream formulation, method of characteristics.
- 2D Euler: global wellposedness, fast growth in vorticity gradient.
- 3D Euler: possible blowup scenarios.
- Second order elliptic equations:
Grades
- The grade will be based on class participation, occational homework assignments, as well as a possible final project.
Contact Information
- Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it..