Our own Marshall Slemrod has just made quite a splash. He's shown that using the Navier-Stokes equations (the fundamental equations of fluid mechanics) to explain the Crookes radiometer, are 'incomplete'. He proposed to use the Korteweg theory to better approximate the Boltzmann equation for gases near vacuum. This is related to Hilbert's 6th problem.

See the article in Quanta Magazine:

https://www.quantamagazine.org/20150721-famous-fluid-equations-are-incomplete/.