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Abstract In this paper the surface quasi-geostrophic equations (QGE) with fractional dissipation in R 2 are considered. Our aim is to study the long-time behavior of solutions of QGE in… Click to show full abstract
Abstract In this paper the surface quasi-geostrophic equations (QGE) with fractional dissipation in R 2 are considered. Our aim is to study the long-time behavior of solutions of QGE in the subcritical case. To this end we investigate the global well-posedness and global attractor for QGE in H s ( R 2 ) via commutator estimates for nonlinear terms, a new iterative technique for estimates of higher order derivatives and with the help of a nonlocal damping term. Besides, by using the fractional Lieb–Thirring inequality, estimates of the finite Hausdorff and fractal dimensions of the global attractor are found.
Journal Title: Journal of Differential Equations
Year Published: 2019
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