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Mathematics > Analysis of PDEs

arXiv:1808.01494 (math)
[Submitted on 4 Aug 2018]

Title:Incompressible impinging jet flow with gravity

Authors:Jianfeng Cheng, Lili Du, Zhouping Xin
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Abstract:In this paper, we investigate steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle, falling under gravity and impinging onto a horizontal wall. More precisely, for any given atmosphere pressure $p_{atm}$ and any appropriate incoming total flux $Q$, we establish the existence of two-dimensional incompressible impinging jet with gravity. The two free surfaces initiate smoothly at the endpoints of the nozzle and become to be horizontal in downstream. By transforming the free boundary problem into a minimum problem, we establish the properties of the flow region and the free boundaries. Moreover, the asymptotic behavior of the impinging jet in upstream and downstream is also obtained.
Comments: 53 Pages
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1808.01494 [math.AP]
  (or arXiv:1808.01494v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1808.01494

Submission history

From: Lili Du [view email]
[v1] Sat, 4 Aug 2018 15:37:37 UTC (407 KB)
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