Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing
Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing
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DOI：
10.2969/jmsj/87148714
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发表时间：
2019-08
影响因子：
0.7
通讯作者：
Mikihiro Fujii
中科院分区：
文献类型：
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作者：
Mikihiro Fujii
如果色散参数的大小足够大，我们考虑具有弱耗散项 $\kappa(-\Delta)^{\alpha/2}\theta\ (0 2-\alpha)$ 的二维准地转方程的初值问题。这种现象就是所谓的全局规律。我们还得到了初始数据与色散参数之间的关系，这保证了全局解的存在。此外，我们还展示了缩放临界Sobolev空间$H^{2-\alpha}(\mathbb{R}^2)$中的全局正则性，并发现确保全局存在的色散参数的大小由每个子集$K\subset H^{2-\alpha}(\mathbb{R}^2)$决定，这在一些齐次Sobolev空间中是预紧的。
We consider the initial value problem for the 2D quasi-geostrophic equation with weak dissipation term $\kappa(-\Delta)^{\alpha/2}\theta\ (0 2-\alpha)$ if the size of dispersion parameter is sufficiently large. This phenomenon is so-called the global regularity. We also obtain the relationship between the initial data and the dispersion parameter, which ensures the existence of the global solution. Moreover, we show the global regularity in the scaling critical Sobolev space $H^{2-\alpha}(\mathbb{R}^2)$ and find that the size of dispersion parameter to ensure the global existence is determined by each subset $K\subset H^{2-\alpha}(\mathbb{R}^2)$, which is precompact in some homogeneous Sobolev spaces.