论文标题
时间周期性的双连接溶液的3D准晶状体模型
Time periodic doubly connected solutions for the 3D quasi-geostrophic model
论文作者
论文摘要
在本文中，我们在斑块设置中为3D准地球模型构建了时间周期性连接的解决方案。更具体地说，我们证明存在非平凡$ m $折叠的双重连接的旋转贴片，该旋转贴片是从通用双重连接的革命形状域，具有较高对称性$ m \ geq m_0 $和$ m_0 $的大小足够大。平衡状态下的线性矩阵算子具有可变和奇异系数，其光谱分析是通过在[27]中设计的方法进行的，其中已引入合适的对称性。由于表面之间的相互作用使光谱问题变得更丰富且参与其中，因此出现了新的困难。
In this paper, we construct time periodic doubly connected solutions for the 3D quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial $m$-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry $m\geq m_0$ and $m_0$ is large enough. The linearized matrix operator at the equilibrium state is with variable and singular coefficients and its spectral analysis is performed via the approach devised in [27] where a suitable symmetrization has been introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved.
