Two-dimensional cavity flow in an infinitely long channel with non-zero vorticity
type: Item
instance of: scholarly article
title: Two-dimensional cavity flow in an infinitely long channel with non-zero vorticity
zbMATH Open document ID: 1379.35096
author: Jianfeng Cheng
author: Lili Du
author: Qin Zhang
published in: Journal of Differential Equations
publication date: 2017-08-03T00:00:00Z
review text: The well-posedness theory of the incompressible inviscid cavity flow in an infinitely long channel is investigated. The flow is governed by a two-dimensional incompressible steady system. By establishing the existence and uniqueness of the incompressible cavity flow in an infinitely long symmetric channel, which contains a smooth free surface detaching at a boundary point of the obstacle, and then pointing out the asymptotic behavior of the cavity flow together with the positivity of the horizontal velocity, the authors finally show that there does not exist a finite cavity or a cusped cavity in an infinitely long nozzle, which gives a positive answer to the \textit{H. Villat} conjecture [Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 3 (5), 375--404 (1913; \url{doi:10.5802/afst.292})] on the non-existence of a finite cusped cavity behind an obstacle.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 76B03
Mathematics Subject Classification ID: 76B10
zbMATH DE Number: 6756310
zbMATH Keywords: inviscid cavity flow
zbMATH Keywords: incompressible Euler system
zbMATH Keywords: existence and uniqueness
MaRDI profile type: Publication
full work available at URL: j.jde.2017.05.013
OpenAlex ID: W2620880028
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DOI: 10.1016/J.JDE.2017.05.013
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description: scientific article; zbMATH DE number 6756310