文献[1]对于水平区域为β-平面上有界区域的三维准地转运动,首次建立了只需确定两维 Laplace 算子最小特征值的非线性稳定性判据,它对应于 Arnold 第二定理.本文通过更加精细的分析、估计,给出了一个新的判据,它优于文献[1]中的结果.在...文献[1]对于水平区域为β-平面上有界区域的三维准地转运动,首次建立了只需确定两维 Laplace 算子最小特征值的非线性稳定性判据,它对应于 Arnold 第二定理.本文通过更加精细的分析、估计,给出了一个新的判据,它优于文献[1]中的结果.在β-平面近似下,三维准地转模式如下:展开更多
For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta...For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta-plane, and to verify it, one needs only to find out the least eigenvalue of a boundary value problem for the 2-D Laplacian. By more accurate estimate and more detailed analysis, this note establishes a new展开更多
基金Project supported by the National Natural Science Foundation of China the French-Chinese Cooperation Programme
文摘For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta-plane, and to verify it, one needs only to find out the least eigenvalue of a boundary value problem for the 2-D Laplacian. By more accurate estimate and more detailed analysis, this note establishes a new
