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 (with respect to the viscosity), while for Besicovitch solutions certain limitations on the generalised Fourier coefficients are requested.

On Leray's problem for almost periodic flows

BERSELLI, LUIGI CARLO;ROMITO, MARCO
2012

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 (with respect to the viscosity), while for Besicovitch solutions certain limitations on the generalised Fourier coefficients are requested.
Berselli, LUIGI CARLO; Romito, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/192853
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