We show, by an explicit construction, the existence of solutions to the Stokes system in dimension three that are singular on a fractal set. The singular points are understood in the sense given by Caffarelli, Kohn and Nirenberg (1982). As an application, we show the existence of suitable weak solutions to the Navier-Stokes equations, driven by rough forces, that are singular on a fractal set.
Some examples of singular fluid flows / Romito, Marco. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 13:1(2006), pp. 67-89.