The seemingly simple problem of determining the drag on a body moving througha very viscous fluid has, for over 150 years, been a source of theoreticalconfusion, mathematical paradoxes, and experimental artifacts, primarilyarising from the complex boundary layer structure of the flow near the body andat infinity. We review the extensive experimental and theoretical literature onthis problem, with special emphasis on the logical relationship betweendifferent approaches. The survey begins with the developments of matchedasymptotic expansions, and concludes with a discussion of perturbativerenormalization group techniques, adapted from quantum field theory todifferential equations. The renormalization group calculations lead to a newprediction for the drag coefficient, one which can both reproduce and surpassthe results of matched asymptotics.
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