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Analysis Seminar

Thursday, February 8, 2024 - 3:30pm

Mimi Dai

University of Illinois at Chicago


University of Pennsylvania

DRL 4E19

The mathematical theory of incompressible fluids still poses challenges for us today. The very basic question of well-posedness remains open for many fluid equations, including the Navier-Stokes equation (NSE) and other related systems. Notably the appearance of singularity of solutions to the 3D NSE in finite time is one of the seven Millennium Problems. We will discuss some recent progress in the effort to understand this classical problem by exploring ill-posedness phenomena, with an emphasis on the construction of pathological solutions which either violate uniqueness or develop finite time singularity. The development relies on some new analytical techniques sparked by empirical laws in physics and novel ideas from other disciplines of mathematics.