Mathematicians Find Wrinkle in Famed Fluid Equations
   Using this approach, Buckmaster and Vicol 
   prove that these very weak solutions to the 
   Navier-Stokes equations are nonunique. They 
   demonstrate, for example, that if you start 
   with a completely calm fluid, like a glass 
   of water sitting still by your bedside, two 
   scenarios are possible. The first scenario 
   is the obvious one: The water starts still 
   and remains still forever. The second is 
   fantastical but mathematically permissible: 
   The water starts still, erupts in the middle
   of the night, then returns to stillness.

Also permissible, and also vanishingly unlikely, under quantum theory.It's a stretch, but I wonder if it's reasonable to think of data points in the vector field describing fluid motion as probabilities rather than definite measurements.  That might allow their behavior to be modeled with different mathematical tools.