Divergent series and hydrodynamics

Hydrodynamics is a very useful theory of near equilibrium dynamics, but it is far from obvious what "near equilibrium" means in practice. Central to the formulation of hydrodynamics is a perturbative series, the gradient expansion. The applicability of hydrodynamics should be related to how well this perturbative expansion works. Many studies have shown that it is actually a divergent series. In this seminar, I'll talk about why it diverges, and why this does not spell the end of hydrodynamics.