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Weak convergence results for inhomogeneous rotating fluid equations

Isabelle Gallagher·Laure Saint-Raymond
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Abstract

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). We prove the weak convergence of Leray--type solutions towards a vector field which satisfies the usual 2D Navier--Stokes equation in the regions of space where B is constant, with Dirichlet boundary conditions, and a heat--type equation elsewhere. The method of proof uses weak compactness arguments.

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Isabelle Gallagher, Laure Saint-Raymond. 2003-02-10. Weak convergence results for inhomogeneous rotating fluid equations. https://arxiv.org/abs/math/0302103

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