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Stability and instability analyses of the dissipative quasi-geostrophic equation. (English) Zbl 1133.76024

Summary: This study examines a spatially periodic fluid flow governed by the dissipative quasi-geostrophic equation

θ t+u·θ+κ(-Δ) α θ=f

for 0<α1. The nonlinear stability and instability analysis focuses on the motion excited by a typical forcing in the study of quasi-geostrophic fluid motions.

MSC:
76E20Stability and instability of geophysical and astrophysical flows
76E30Nonlinear effects (fluid mechanics)
35Q35PDEs in connection with fluid mechanics