It is well known how to construct a Laplacian on a fractal using Dirichlet forms (see e.g.
[the survey article][1] by Strichartz). This implies, in particular, that a fractal can be "heated", i.e. one can write (and solve) the heat equation on the fractal.

**The question is**, can one run a fluid flow through a fractal set? In other words, is there
a proper way to write the Navier-Stokes equations on a fractal? In order to do this, it seems that  we need a "correct" notion of *divergence* at least.

More generally, *is there a "correct" way to define a differential form on a fractal?*


  [1]: http://www.ams.org/notices/199910/fea-strichartz.pdf