Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in R2
Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in R2
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DOI：
10.1016/j.jde.2018.11.009
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发表时间：
2019-05
影响因子：
2.4
通讯作者：
R. Farwig;C. Qian
中科院分区：
文献类型：
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作者：
R. Farwig;C. Qian
本文研究了R2中具有分数阶耗散的地表准地转方程。我们的目的是研究亚临界情形下QGE解的长时间行为。为此，我们调查的整体适定性和整体吸引子QGE在HS（R2）通过交换器估计的非线性项，一种新的迭代技术估计高阶导数和帮助的非局部阻尼项。此外，利用分数阶Lieb-Thirring不等式，得到了全局吸引子的有限Hausdorff维数和分形维数的估计.
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.