Boundary layer analysis for the fast horizontal rotating fluids

Chao-Jiang Xu (Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China; and Laboratoire de Mathématiques, Université de Rouen Normandie, Saint-Etienne du Rouvray, France)

Abstract

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.

Keywords

incompressible Navier–Stokes equation, boundary layer, rotating fluids

2010 Mathematics Subject Classification

35M13, 35Q30, 35Q35, 76U05

Full Text (PDF format)

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