论文标题
$ 2 $ d Quasi-Geostophic方程的时间周期性解决方案，并具有超临界的耗散
Time periodic solutions to the $2$D quasi-geostrophic equation with the supercritical dissipation
论文作者
论文摘要
我们考虑使用时间周期性外力的$ 2 $ d耗散的准地球化方程，并证明在超临界耗散的情况下存在独特的时间周期性解决方案。在这种情况下，耗散项产生的半群的平滑效应太弱，无法控制correponding积分方程的Duhamel项中的非线性。在本文中，我们提供了一种新方法，不取决于积分方程的收缩映射原理。
We consider the $2$D 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 correponding integral equation. In this paper, we give a new approach which does not depend on the contraction mapping principle for the integral equation.
