Multifractal scaling and the Euler equations on R^3/Z^3

We study the Euler equations describing the motion of an incompressible fluid on the cubic torus with real initial data. We construct solutions on the Fourier side which display a sudden loss of regularity within finite time even for highly regular initial data. Moreover, the solution may regain its initial regularity within finite time. This loss of regularity may coincide with the appearance of a certain type of multifractal scaling of the solutions.