The Unstable Spectrum of the Surface Quasi-Geostrophic Equation
The Unstable Spectrum of the Surface Quasi-Geostrophic Equation
复制标题
地表准地转方程的不稳定谱
DOI：
10.1007/s00021-004-0129-3
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
R. Shvydkoy
中科院分区：
文献类型：
--
作者：
S. Friedlander;R. Shvydkoy
摘要：我们研究了地球物理流体动力学中出现的一个方程的不稳定谱，这个方程被称为表面准地转方程。一般来说，谱是离散特征值和本质谱的结合。我们证明了存在的不稳定特征值在一个特定的例子。我们研究了半群的谱和演化算子。我们展示了这些频谱的结构一般流，并证明了频谱映射定理成立。我们观察到，SQG方程的谱性质是密切类似的二维欧拉方程。
Abstract.We study the unstable spectrum of an equation that arises in geophysical fluid dynamics known as the surface quasi-geostrophic equation. In general the spectrum is the union of discrete eigenvalues and an essential spectrum. We demonstrate the existence of unstable eigenvalues in a particular example. We examine the spectra of the semigroup and the evolution operator. We exhibit the structure of these spectra for general flows and prove that a spectral mapping theorem holds. We observe that the spectral properties of the SQG equation are closely analogous to those of the two-dimensional Euler equation.