Nonlinear boundary layers for rotating fluids
Analysis of PDEs
2015-11-06 v1
Abstract
We investigate the behavior of rotating incompressible flows near a non-flat horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple linear ODE. When bottom variations are taken into account, it is governed by a nonlinear PDE system, with far less obvious mathematical properties. We establish the well-posedness of this system and the asymptotic behavior of the solution away from the boundary. In the course of the proof, we investigate in particular the action of pseudo-differential operators in non-localized Sobolev spaces. Our results extend the older paper [18], restricted to periodic variations of the bottom. It ponders on the recent linear analysis carried in [14].
Cite
@article{arxiv.1511.01856,
title = {Nonlinear boundary layers for rotating fluids},
author = {Anne-Laure Dalibard and David Gérard-Varet},
journal= {arXiv preprint arXiv:1511.01856},
year = {2015}
}