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Nonlinear stability criteria for the motion of three-dimensional quasigeostrophic flow on a \(\beta\)-plane. (English) Zbl 0742.76037

Summary: This paper is concerned with the nonlinear stability of three-dimensional quasigeostrophic motion on a \(\beta\)-plane. The criteria obtained here are applicable to perturbations of both initial data and parameters in models. For verifying criteria parallel to Arnold’s second theorem given by other authors, one has to calculate the lowest eigenvalue of a three- dimensional elliptic partial differential equation with variable coefficients and, for our criteria, one only needs to do the same for the two-dimensional Laplacian.

MSC:

76E30 Nonlinear effects in hydrodynamic stability
35P15 Estimates of eigenvalues in context of PDEs
76E20 Stability and instability of geophysical and astrophysical flows
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