Existence and non-existence of time-periodic solutions to the Navier-Stokes equations (Harmonic Analysis and Nonlinear Partial Differential Equations)

This note is a survey of the paper [7], where the author constructed a unique small time-periodic solution for the incompressible Navier-Stokes equations with time-periodic external forces in ℝ^𝓃 with 𝓃 3 in the scaling critical spaces of Besov type, while the non-existence of time-periodic solutions was established in the two-dimensional case.