Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation.

We consider the SQG equation with dissipation given by a fractional Laplacian of order α < 1 2 . We introduce a notion of suitable weak solution, which exists for every L 2 initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most 1 2 α 1 + α α ( 1 - 2 α ) + 2 .