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| I will discuss the application of time-averaging in getting rigorous error estimates of some reduced fluid models, including the quasi-geostrophic approximation, incompressible approximation and zonal flows. The spatial boundary can be present as a non-penetrable solid wall. I will show a very recent (and somewhat surprising) result on the $\epsilon^2$ accuracy of incompressible approximation of Euler equations, thanks to several decoupling properties. |
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