On Leray's problem for almost periodic flows

2010/12/08 by Luigi C. Berselli, Berselli, Luigi C., Marco Romito +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B15 #35Q30 #76D03 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1012.1726

openalex publication_date 2010/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Pulsatile Flows for Simplified Smart Fluids with Variable Power-Law: Analysis and Numerics

Related

• A Remark on the Leray's Problem on Stationary Navier-Stokes Flows with Large Fluxes in Infinite Cylindrical Domains
• Almost periodic structures and the semiconjugacy problem
• A refined uniqueness result of Leray's problem in an infinite-long pipe with the Navier-slip boundary
• Leray's plane stationary solutions at small Reynolds numbers
• Periodic Lp estimates by R-boundedness: Applications to the Navier-Stokes equations