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Existence of solutions for the Navier-Stokes equations, having an infinite dissipation of energy, in a class of domains with noncompact boundaries

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Abstract

In the domain Ω ∋ ℝ3 with two exits at infinity, Ω1 = {x:∣x′∣<g 1(x 3),x 3 > 2} and Ω2 = {x:0<x 3<g 3(∣x′∣), ∣x′∣>2}, one investigates the stationary system of Navier-Stokes equations under the boundary condition

. One proves existence and uniqueness theorems for the solution of this problem with an infinite Dirichlet integral, under a given flow of the velocity vector across the cross sections of the exits at infinity. As an example one considers the case wheng i(t) ≡1.

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Literature cited

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Authors
  1. K. I. Piletskas
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 180–202, 1981.

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Piletskas, K.I. Existence of solutions for the Navier-Stokes equations, having an infinite dissipation of energy, in a class of domains with noncompact boundaries. J Math Sci 25, 932–948 (1984). https://doi.org/10.1007/BF01788925

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