Abstract
The critical and super-critical dissipative quasi-geostrophic equations are investigated in \(\mathbb{R}^2\). We prove local existence of a unique regular solution for arbitrary initial data in H 2-2α which corresponds to the scaling invariant space of the equation. We also consider the behavior of the solution near t = 0 in the Sobolev space.
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Miura, H. Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space. Commun. Math. Phys. 267, 141–157 (2006). https://doi.org/10.1007/s00220-006-0023-3
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DOI: https://doi.org/10.1007/s00220-006-0023-3