Spring 2026
Yanyan Li
Subtitle:
The Incompressible Navier-Stokes Equations, Focusing on Stationary Solutions
Course Description:
This course presents selected topics concerning the incompressible Navier–Stokes equations, with particular emphasis on stationary (steady-state) problems. We will develop the mathematical tools needed to understand classical and modern results in the area. Foundational material from partial differential equations—including Sobolev spaces, embedding theorems, and elements of the Leray–Schauder degree theory—will be reviewed as needed.
1. Overview and exposition of the existence theory for nonhomogeneous stationary Navier–Stokes equations in two dimensions.
This includes Leray’s pioneering work and several significant developments from the last few years.
2. Overview and exposition of Leray’s problem for steady Navier–Stokes flow past a body in the plane.
3. Regularity of solutions of stationary Navier-Stokes in R^n for n \le 15.
Text:
[MB] A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics, Vol. 27, Cambridge University Press, 2002. [G] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations: Steady-State Problems, Second Edition, Springer Monographs in Mathematics, Springer, 2011. [KPR] M. Korobkov, K. Pileckas, and R. Russo, The Steady Navier–Stokes System: Basics of the Theory and the Leray Problem, Advances in Mathematical Fluid Mechanics, Birkhäuser, 2024.
Prerequisites:
640:517 or permission of the instructor
Schedule of Sections:
16:640:519 Schedule of Classes
Previous Semesters:
- Spring 2026 - Li, Yanyan
- Fall 2024 - Feehan, Paul
- Spring 2024 - Sesum, Natasa
- Spring 2022 - Li, Yanyan
- Spring 2020 Prof. Sesum