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- W2963454495 endingPage "2018" @default.
- W2963454495 startingPage "1997" @default.
- W2963454495 abstract "This paper is devoted to the global (in time) regularity problem for a family of active scalar equations with fractional dissipation. Each component of the velocity field $u$ is determined by the active scalar $theta$ through $mathcal{R} Lambda^{-1} P(Lambda) theta$ where $mathcal{R}$ denotes a Riesz transform, $Lambda=(-Delta)^{1/2}$ and $P(Lambda)$ represents a family of Fourier multiplier operators. The 2D Navier-Stokes vorticity equations correspond to the special case $P(Lambda)=I$ while the surface quasi-geostrophic (SQG) equation to $P(Lambda) =Lambda$. We obtain the global regularity for a class of equations for which $P(Lambda)$ and the fractional power of the dissipative Laplacian are required to satisfy an explicit condition. In particular, the active scalar equations with any fractional dissipation and with $P(Lambda)= (log(I-Delta))^gamma$ for any $gamma>0$ are globally regular." @default.
- W2963454495 created "2019-07-30" @default.
- W2963454495 creator A5037968657 @default.
- W2963454495 creator A5041354678 @default.
- W2963454495 creator A5088414276 @default.
- W2963454495 date "2012-01-01" @default.
- W2963454495 modified "2023-09-26" @default.
- W2963454495 title "Dissipative Models Generalizing the 2D Navier-Stokes and the Surface Quasi-Geostrophic Equations" @default.
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