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Imperfect bifurcation for the quasi-geostrophic shallow-water equations. (English) Zbl 1409.76036

This is a piece of nice analytical and numerical work. Fluid by nature is ever changing, as a result, the fluid equations usually display turbulent solutions. Stationary or steady solutions of fluid equations are usually trivial. The stationary uniform vorticity patches are interesting steady solutions, which can have various applications. This work demonstrates bifurcation patterns near these stationary vortex patches based on the Crandall-Rabinowitz theorem. Numerical simulation of the problem is also challenging, and the current work pushes the numerical simulation to an impressive stage.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76M99 Basic methods in fluid mechanics
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