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research article
Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
March 26, 2021
We 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))).
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Colombo-Haffter2021_Article_EstimateOnTheDimensionOfTheSin.pdf
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