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This seminar in Analysis and Geometry covers the topic of the non-uniqueness of Leray solutions of the forced Navier-Stokes equations. The course aims to explore suitable weak solutions, progress on the problem, the main theorem, unstable manifold, similarity variables, two-dimensional instability, construction of the unstable vortex, neutral limiting modes, vortex rings, axisymmetric Euler equations, linearized Euler operators, and a single function space. The teaching method includes lecture notes, discussions, and addressing questions. This course is intended for individuals interested in advanced topics in mathematics, particularly in the field of fluid dynamics and partial differential equations.
