论文标题
3D准地藻模型的时间周期解决方案
Time periodic solutions for 3D quasi-geostrophic model
论文作者
论文摘要
本文旨在研究3D Inviscid准地球模型的时间周期性解决方案。我们通过在垂直轴周围的通用革命形状给出的固定溶液的适当扰动来显示非琐碎旋转斑块的存在。这些特殊解决方案的构建是通过分叉理论完成的。通常，光谱问题非常细腻，很大程度上取决于初始固定溶液的形状。更具体地说，光谱研究可能与自动化紧凑型操作员的特征值问题有关。我们只能从操作员最大的特征值实施分叉，这很简单。通过使用Dirichlet边界条件类型的合适功能空间和具有各向异性核的精制势能理论，解决了极点的奇异性产生的其他困难。
This paper aims to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. More specifically, the spectral study can be related to an eigenvalue problem of a self-adjoint compact operator. We are able to implement the bifurcation only from the largest eigenvalues of the operator, which are simple. Additional difficulties generated by the singularities of the poles are solved through the use of suitable function spaces with Dirichlet boundary condition type and refined potential theory with anisotropic kernels.
