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• W2991247473 abstract "In this paper, we consider the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and fractional vertical thermal diffusion. Global existence of classical solutions is established when the dissipation powers are restricted to a suitable range. Due to the nonlocality of these 1D fractional operators, some of the standard energy estimate techniques no longer apply, to overcome this difficulty, we establish several anisotropic embedding and interpolation inequalities involving fractional derivatives. In addition, in order to bypass the unavailability of the classical Gronwall inequality, we establish a new logarithmic type Gronwall inequality, which may be of independent interest and potential applications." @default.
• W2991247473 created "2019-12-05" @default.
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• W2991247473 date "2019-11-19" @default.
• W2991247473 modified "2023-09-24" @default.
• W2991247473 title "On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation" @default.
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• W2991247473 doi "https://doi.org/10.1088/1361-6544/ab41e6" @default.
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