The Incompressible Navier–Stokes Equations: Stationary Solutions
讲课人：李岩岩教授（美国Rutgers大学）
课程时间：7月9、13、15、22、24日，每天10:00–12:00
地点：教四108
课程内容: This minicourse will present selected topics in the mathematical theory of the incompressible Navier–Stokes equations, with an emphasis on stationary, or steady-state, solutions. The aim is to introduce several fundamental problems, explain the main analytical ideas behind their study, and discuss both classical results and recent developments.
The course will focus on the following topics:
• Nonhomogeneous stationary Navier–Stokes equations in two dimensions. We will give an overview of the existence theory, beginning with Leray’s pioneering work and continuing with several significant recent developments.
• Leray’s problem for steady flow past an obstacle in the plane. We will discuss the formulation of the problem, the principal mathematical difficulties, and the main ideas and results concerning existence and behavior at infinity.
• Regularity of stationary Navier–Stokes solutions in higher dimensions. We will present recent regularity results for stationary solutions in
, with particular attention to the range 
.
Relevant analytical tools—including Sobolev spaces, embedding theorems, a priori estimates, compactness methods, and elements of Leray–Schauder degree theory—will be introduced or reviewed as needed. The minicourse is intended for advanced undergraduate students and graduate students with a basic background in partial differential equations and functional analysis.
