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- W4328119030 abstract "Abstract We prove the global regularity of smooth solutions for a dissipative surface quasi-geostrophic (SQG) equation with both velocity and dissipation logarithmically supercritical compared to the critical equation. By this, we mean that a symbol defined as a power of logarithm is added to both velocity and dissipation terms to penalize the equation’s criticality. Our primary tool is the nonlinear maximum principle which provides transparent proofs of global regularity for nonlinear dissipative equations. Combining the nonlinear maximum principle with a modulus of continuity, we prove an uniform-in-time gradient estimate for the critical and slightly supercritical SQG equation. It improves the previous double exponential bound by Kiselev–Nazarov–Volberg to the single exponential. In addition, we prove the eventual exponential decay of the solutions." @default.
- W4328119030 created "2023-03-22" @default.
- W4328119030 creator A5087204456 @default.
- W4328119030 date "2023-03-21" @default.
- W4328119030 modified "2023-10-14" @default.
- W4328119030 title "Global well-posedness of slightly supercritical SQG equations and gradient estimate" @default.
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- W4328119030 doi "https://doi.org/10.1088/1361-6544/acc2a6" @default.
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