An Almanack

Terrence Tao has made some deep observations on why the regularity of three dimensional Navier-Stokes is such a hard problem. Although he has gone on to many other equally interesting topics, I remain fascinated by his main point there: that Navier-Stokes is supercritical. The nonlinearities become stronger at small distance scales, making it impossible to know (using present techniques) whether solutions remain smooth for all time. Thus, it is crucial to understand the scale dependence of non-linearities in fluid mechanics.
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