Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space

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Well-posedness for a transport equation with nonlocal velocity (2008, methodology): “We shall use the next two standard linear estimates, the proofs of which can be found, for example, in [15].”
On the global regularity for the supercritical SQG equation (2014, background): “Specifically, [9, 12, 15, 21, 26] deal with the Sobolev space setting, showing that small initial data (with respect to the viscosity coefficient, here normalized to 1) in X = H2−γ lead to the global existence of solutions.”
Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness (2007, methodology): “Proof of Theorem 1.5: The proofs of the first part of the theorem and the second part for � ∈ [0,) can be found in [ 17 ].”
Nonuniqueness of Weak Solutions to the SQG Equation (2016, background): “6 The finite-time blowup cannot occur for sufficiently smooth and small initial data [34,59,70,87], and as ! 1 it also cannot happen for data that is large, but not exceedingly large [40].”