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Weak convergence results for inhomogeneous rotating fluid equations. (English) Zbl 1132.35440
Summary: We consider the equations governing incompressible, viscous fluids in three space dimensions, rotating around an inhomogeneous vector \(B(x)\); this is a generalization of the usual rotating fluid model (where \(B\) is constant). In the case n which \(B\) has non-degenerate critical points, we prove the weak convergence of Leray-type solutions towards a vector field which satisfies a heat equation as the rotation rate tends to infinity. The method of proof uses weak compactness arguments, which also enable us to recover the usual 2D Navier-Stokes limit in the case when \(B\) is constant.

MSC:
35Q35 PDEs in connection with fluid mechanics
35D05 Existence of generalized solutions of PDE (MSC2000)
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
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