Communications in Mathematical Sciences
Volume 17 (2019)
Boundary layer analysis for the fast horizontal rotating fluids
Pages: 299 – 338
It is well known that, for fast rotating fluids with the axis of rotation being perpendicular to the boundary, the boundary layer is of Ekman-type, described by a linear ODE system. In this paper we consider fast rotating fluids, with the axis of rotation being parallel to the boundary. We show that, for certain initial data with special asymptotic expansion, the corresponding boundary layer is described by a nonlinear, degenerated PDE system which is similar to the 2D Prandtl system. Finally, we prove the well-posedness of the governing system of the boundary layer in the space of analytic functions with respect to tangential variable.
incompressible Navier–Stokes equation, boundary layer, rotating fluids
2010 Mathematics Subject Classification
35M13, 35Q30, 35Q35, 76U05
The research of the first author was supported by NSF of China(11871054,11771342) and Fok Ying Tung Education Foundation (151001), and he would like to thank the invitation of the “Laboratoire de mathématiques Raphaël Salem” of the Université de Rouen Normandie. The second author would like to express his sincere thanks to the School of mathematics and statistics of Wuhan University for the invitations. The research of the last author is supported partially by “The Fundamental Research Funds for Central Universities of China”.
Received 22 June 2018
Received revised 28 November 2018
Accepted 28 November 2018
Published 8 July 2019