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Anisotropy and dispersion in rotating fluids. (English) Zbl 1034.35107

Cioranescu, Doina (ed.) et al., Nonlinear partial differential equations and their applications. Collège de France seminar. Vol. XIV. Lectures held at the J. L. Lions seminar on applied mathematics, Paris, France, 1997–1998. Amsterdam: Elsevier (ISBN 0-444-51103-2/hbk). Stud. Math. Appl. 31, 171-192 (2002).
The authors study dispersion phenomena occuring in singular perturbation models of fluid dynamics. More precisely, they examine the small Rossby number limit of solutions to incompressible Navier-Stokes equations in three dimensions. The convergence to the corresponding limiting two-dimensional Navier-Stokes equations is proved by using anisotropic Strichartz-type estimates which take into account viscosity effects.
For the entire collection see [Zbl 0992.00032].

MSC:

35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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