Time-periodic Poiseuille-type solution with minimally regular flow rate
2021 ◽
Vol 26
(5)
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pp. 947-968
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The nonstationary Navier–Stokes equations are studied in the infinite cylinder Π = {x = (x', xn) ∈ Rn: x' ∈ σ ∈ R 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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2018 ◽
pp. 121-144
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2017 ◽
pp. 77-137
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2016 ◽
Vol 36
(4)
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pp. 1015-1029
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Keyword(s):
2007 ◽
Vol 20
(2)
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pp. 301-335
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2002 ◽
Vol 465
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pp. 213-235
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2007 ◽
Vol 571
◽
pp. 265-280
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