On Leray's problem for almost periodic flows
Abstract
We prove existence and uniqueness for fully-developed (Poiseuille-type) flows in semi-infinite cylinders, in the setting of (time) almost-periodic functions. In the case of Stepanov almost-periodic functions the proof is based on a detailed variational analysis of a linear "inverse" problem, while in the Besicovitch setting the proof follows by a precise analysis in wave-numbers. Next, we use our results to construct a unique almost periodic solution to the so called "Leray's problem" concerning 3D fluid motion in two semi-infinite cylinders connected by a bounded reservoir. In the case of Stepanov functions we need a natural restriction on the size of the flux, while for Besicovitch solutions certain limitations on the generalized Fourier coefficients are requested.
Keywords
Cite
@article{arxiv.1012.1726,
title = {On Leray's problem for almost periodic flows},
author = {Luigi C. Berselli and Marco Romito},
journal= {arXiv preprint arXiv:1012.1726},
year = {2010}
}