Campus, PAB 232
As physicists, when we arrive at a differential equation, the hard part of the problem is essentially over. We simply look up the form of the solution and apply the boundary condit-- wait. The mathematicians haven’t figured this one out yet? It is a famous open problem in mathematics to disprove that smooth and bounded solutions to the Naiver-Stokes equation in three dimensions even exist. This implies that aerospace engineers designing rocket ships must rely on “simulations” which I will not talk about. Instead, I will describe how turbulent and chaotic behavior can arise from basic physical assumptions like the continuity equation, and give a description of the Kolmogorov similarity hypotheses, which are statistical heuristics used to sweep all of that complexity under the rug. If time permits, we might even prove the two different views are consistent.