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

Colombo, Maria CarolaHaffter, Silja Noëmi Aline2021-04-062021-04-062021-04-062021-03-2610.1007/s40818-021-00093-3https://infoscience.epfl.ch/handle/20.500.14299/177021We consider the SQG equation with dissipation given by a fractional Laplacian of order α<12. We introduce a notion of suitable weak solution, which exists for every L2 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 1/2α(((1+α/α)((1−2α)+2))).Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equationtext::journal::journal article::research article