A New Course: Navier-Stokes Equations with a Historical Perspective

A new class was developed at the University of Florida within the Department of Mechanical and Aerospace Engineering called the Navier-Stokes equations. The goal of the course is to explain contemporary challenges and state-of-the-art analysis for students in engineering and mathematics. The course covers Navier-Stokes equations, history, derivation, physical meaning, classical solutions, stability, dynamical systems, existence, uniqueness, regularity, scales, ladder results, dissipation rates, Serrin's blowup, capacitary approaches, mild solutions (Lebesgue, Sobolev, Besov, Morrey, BMO, Koch, Tataru), weak solutions, stochastics, the Russian school, and invariant measures. Student assessment is conducted via analysis assignments, term papers, and a presentation on a topic of their choice. Feedback from students and progress on making the course publicaly available are presented. The course makes available freely a 1,768 page PDF handout with 2,004 unique equations and 92 historical figures.