Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation
Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation
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DOI：
10.1007/s00028-022-00787-6
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发表时间：
2020-06
影响因子：
1.4
通讯作者：
Mikihiro Fujii
中科院分区：
文献类型：
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作者：
Mikihiro Fujii
我们考虑具有时间周期外力的二维耗散准地转方程，并证明了超临界耗散情况下唯一时间周期解的存在性。在这种情况下，耗散项生成的半群的平滑效果太弱，无法控制相应积分方程的杜哈梅尔项中的非线性。在本文中，我们给出了一种不依赖于积分方程收缩映射原理的新方法。
We consider the 2D dissipative quasi-geostrophic equation with the time periodic external force and prove the existence of a unique time periodic solution in the case of the supercritical dissipation. In this case, the smoothing effect of the semigroup generated by the dissipation term is too weak to control the nonlinearity in the Duhamel term of the corresponding integral equation. In this paper, we give a new approach which does not depend on the contraction mapping principle for the integral equation.