The Navier-Stokes and Euler equations form the cornerstone of fluid dynamics. This talk is concerned with three fundamental challenges in the mathematical analysis of these equations—namely, the global regularity of incompressible Navier-Stokes flows (a Millennium Problem), the Leray problems for stationary Navier-Stokes equations, and thehydrodynamic stability of Euler flows. I will present our recent progress on these problems, including:
(1) Quantitative partial regularity theory, improving the classical result of Caffarelli-Kohn-Nirenberg (1982)
(2) A geometric characterization of potential singularities, which extends the paradigm of Constantin-Fefferman (1993) connecting vorticity alignment and regularity
(3) A complete well-posedness theory for the 2D stationary Navier-Stokes equations at small Reynolds numbers
Global stability of the “rigid body” rotational solution to the 3D Euler equations
讲座地点临时调整，改到光华楼东辅楼101，敬请知悉。
