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Long Time Existence and Asymptotic Behavior of Solutions for the 2D Quasi-geostrophic Equation with Large Dispersive Forcing
Journal of Mathematical Fluid Mechanics ( IF 1.3 ) Pub Date : 2020-11-23 , DOI: 10.1007/s00021-020-00540-4
Mikihiro Fujii

We consider the initial value problem of the 2D dispersive quasi-geostrophic equation. We prove the long time existence of the solution for given initial data \(\theta _0 \in H^s(\mathbb {R}^2)\) with \(s>2\). Moreover, we show that the solution converges to the corresponding linear dispersive solution \(e^{-AtR_1}\theta _0\) when the size of dispersion parameter goes to infinity.



中文翻译:

具有较大色散强迫的二维拟地转方程的解的长时间存在性和渐近性

我们考虑二维色散准地转方程的初值问题。我们用\(s> 2 \)证明了给定初始数据\(\ theta _0 \ in H ^ s(\ mathbb {R} ^ 2)\)中解决方案的长期存在。此外,我们表明,当色散参数的大小达到无穷大时,解收敛于相应的线性色散解\(e ^ {-AtR_1} \ theta _0 \)

更新日期:2020-11-25
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