Symmetries of Navier-Stokes Equations

This lecture covers the symmetries of the Navier-Stokes equations, including the preservation of symmetry in dynamics, spontaneous symmetry breaking, and the periodic boundary conditions. It also discusses the known symmetries, such as translations, Galilean transformations, rotations, and scaling. The lecture emphasizes the importance of symmetry restoration at high Reynolds numbers and the invariance of periodic boundary conditions. Various proofs and examples are provided to illustrate the symmetries and their implications.