Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges
(2021) In Journal of Differential Equations 274. p.345-381- Abstract
We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992) [1]. The domains we consider have a boundary consisting of three parts, one where fluid flows into the domain, one where the fluid flows out, and one which no fluid passes through. These three parts meet at right angles. An example of this would be a right cylinder with fluid flowing in at one end and out at the other, with no fluid going through the mantle. A large part of the proof is dedicated to studying the Poisson equation and the related compatibility conditions required for solvability in this kind of domain.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8c138cd6-5207-4188-a89c-925a4e36ece6
- author
- S. Seth, Douglas LU
- organization
- publishing date
- 2021-02-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Fluid dynamics, Nonsmooth domains, Partial differential equations, Steady Euler equations, Vorticity
- in
- Journal of Differential Equations
- volume
- 274
- pages
- 345 - 381
- publisher
- Elsevier
- external identifiers
-
- scopus:85096872219
- ISSN
- 0022-0396
- DOI
- 10.1016/j.jde.2020.11.034
- project
- Mathematical aspects of three-dimensional water waves with vorticity
- language
- English
- LU publication?
- yes
- id
- 8c138cd6-5207-4188-a89c-925a4e36ece6
- date added to LUP
- 2020-12-14 09:15:32
- date last changed
- 2022-04-26 22:31:35
@article{8c138cd6-5207-4188-a89c-925a4e36ece6,
abstract = {{<p>We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992) [1]. The domains we consider have a boundary consisting of three parts, one where fluid flows into the domain, one where the fluid flows out, and one which no fluid passes through. These three parts meet at right angles. An example of this would be a right cylinder with fluid flowing in at one end and out at the other, with no fluid going through the mantle. A large part of the proof is dedicated to studying the Poisson equation and the related compatibility conditions required for solvability in this kind of domain.</p>}},
author = {{S. Seth, Douglas}},
issn = {{0022-0396}},
keywords = {{Fluid dynamics; Nonsmooth domains; Partial differential equations; Steady Euler equations; Vorticity}},
language = {{eng}},
month = {{02}},
pages = {{345--381}},
publisher = {{Elsevier}},
series = {{Journal of Differential Equations}},
title = {{Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges}},
url = {{http://dx.doi.org/10.1016/j.jde.2020.11.034}},
doi = {{10.1016/j.jde.2020.11.034}},
volume = {{274}},
year = {{2021}},
}