Time-periodic Poiseuille-type solution with minimally regular flow rate
Articles
Kristina Kaulakytė
Vilnius University
https://orcid.org/0000-0002-4718-1000
Nikolajus Kozulinas
Vilnius University
https://orcid.org/0000-0002-4543-721X
Konstantin Pileckas
Vilnius University
https://orcid.org/0000-0003-3256-3388
Published 2021-09-01
https://doi.org/10.15388/namc.2021.26.24502
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Keywords

Navier–Stokes equations
cylindrical domain
time-periodic Poiseuille-type solution
inverse problem
minimal regularity

How to Cite

Kaulakytė K., Kozulinas N. and Pileckas K. (2021) “Time-periodic Poiseuille-type solution with minimally regular flow rate”, Nonlinear Analysis: Modelling and Control, 26(5), pp. 947-968. doi: 10.15388/namc.2021.26.24502.

Abstract

The nonstationary Navier–Stokes equations are studied in the infinite cylinder Π = {x = (x', xn) ∈ Rnx' ∈ σR n – 1: – ∞ < xn < ∞, n = 2, 3} under the additional condition of the prescribed time-periodic flow-rate (flux) F(t). It is assumed that the flow-rate F belongs to the space L2(0, 2π), only. The time-periodic Poiseuille solution has the form u(x, t) = (0, ... , 0, U(x', t)),  p(x,t) = –q(t)xn + p0(t), where (U(x', t), q(t)) is a solution of an inverse problem for the time-periodic heat equation with a specific over-determination condition. The existence and uniqueness of a solution to this problem is proved.

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