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2019 Steady Navier-Stokes equations with Poiseuille and Jeffery-Hamel flows in $\mathbb R^2$
Teppei Kobayashi
Rocky Mountain J. Math. 49(6): 1909-1929 (2019). DOI: 10.1216/RMJ-2019-49-6-1909

Abstract

We consider a steady flow of an incompressible viscous fluid in a two-dimensional unbounded domain with unbounded boundaries. The domain has two outlets. The part of the domain upstream is a cylinder and the part of the domain downstream is a wedge. In the part of the domain upstream, the velocity is required to approach the Poiseuille flow. In the part of the domain downstream, the velocity is required to approach Jeffery-Hamel's flow. This problem has been treated by C.J. Amick and L.E. Frankel, V.A. Solonnikov and many others. Recently, T. Kobayashi obtained the unique solution of Jeffery-Hamel's flows in a wedge. Therefore we reconsider this problem. In this paper, we succeed in proving the existence of such a steady flow under the restricted flux condition which depends only on the part of the domain upstream and downstream.

Citation

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Teppei Kobayashi. "Steady Navier-Stokes equations with Poiseuille and Jeffery-Hamel flows in $\mathbb R^2$." Rocky Mountain J. Math. 49 (6) 1909 - 1929, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1909

Information

Published: 2019
First available in Project Euclid: 3 November 2019

zbMATH: 07136586
MathSciNet: MR4027241
Digital Object Identifier: 10.1216/RMJ-2019-49-6-1909

Subjects:
Primary: 35Q30
Secondary: 76D05

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 6 • 2019
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