2024-03-28T16:19:19Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00040028
2022-12-19T04:13:23Z
312:6865:6899:6907
9:504:6868:6901:6908
On Leray's Problem for Almost Periodic Flows
Berselli, Luigi C.
92472
Romito, Marco
92473
415
Almost periodic flux
channel flow
Leray's problem
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.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
2012-06-20
application/pdf
Journal of mathematical sciences, the University of Tokyo
1
19
69
130
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40028/files/jms190103.pdf
eng