On Some Singular Limits Arising in Fluid Dynamic Modelling

Abstract Fluid dynamic equations are used to model various phenomena arising from physics, engineering, astrophysics, geophysics. One feature is that they take place at different time and length scales it important understand which occur according the use of single or interactions them. From a mathematical point view, these physical behaviours give rise singular limits and, consequently analysis asymptotic state governing equations. In this paper we will analyse very simplified given by linearised continuity equation classical momentum include terms into account rotation show, values scales, behaviour be those an incompressible fluid geostrophic flow. Finally out, set analysed in may also fit artificial compressibility approximation methods.