Simple viscous flows: From boundary layers to the renormalization group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. The extensive experimental and theoretical literature on this problem is reviewed, with special emphasis on the logical relationship between different approaches. The survey begins with the development of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization-group techniques, adapted from quantum field theory to differential equations. The renormalization-group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics.