El Naschie’s ε(∞) space–time and scale relativity theory in the topological dimension D = 3

A scale relativity theory in the topological dimension D = 3 is developed and its corresponding hydrodynamic model is discussed. Some possibilities of the theory and the connection to El Naschie’s ε(∞) space–time by means of a Korteweg–de Vries type equation for an incompressible fluid are established.