Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges

Douglas S. Seth

doi:10.1016/j.jde.2020.11.034

Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges

Douglas S. Seth

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	345-381
Journal	Journal of Differential Equations
Volume	274
Early online date	2020 Nov 24
DOIs	https://doi.org/10.1016/j.jde.2020.11.034
Publication status	Published - 2021 Feb 15

Subject classification (UKÄ)

Mathematical Analysis

Free keywords

Fluid dynamics
Nonsmooth domains
Partial differential equations
Steady Euler equations
Vorticity

Access to Document

10.1016/j.jde.2020.11.034Licence: CC BY-NC-ND

1 Doctoral Thesis (compilation)

On Steady Water Waves and Flows with Vorticity in Three Dimensions
Svensson Seth, D., 2021, Lund: Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics. 225 p.
Research output: Thesis › Doctoral Thesis (compilation)

File

1 Finished

3DWATERWAVES: Mathematical aspects of three-dimensional water waves with vorticity
Wahlén, E. (PI), Pasquali, S. (Researcher), Weber, J. (Researcher), Svensson S, D. (Research student), Lokharu, E. (Researcher) & Varholm, K. (Researcher)
European Commission - Horizon 2020
2016/03/01 → 2022/02/28
Project: Research

Cite this

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title = "Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges",

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.",

keywords = "Fluid dynamics, Nonsmooth domains, Partial differential equations, Steady Euler equations, Vorticity",

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doi = "10.1016/j.jde.2020.11.034",

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T1 - Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges

AU - S. Seth, Douglas

PY - 2021/2/15

Y1 - 2021/2/15

N2 - 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.

AB - 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.

KW - Fluid dynamics

KW - Nonsmooth domains

KW - Partial differential equations

KW - Steady Euler equations

KW - Vorticity

U2 - 10.1016/j.jde.2020.11.034

DO - 10.1016/j.jde.2020.11.034

M3 - Article

AN - SCOPUS:85096872219

SN - 0022-0396

VL - 274

SP - 345

EP - 381

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges

Abstract

Subject classification (UKÄ)

Free keywords

Access to Document

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Research output

On Steady Water Waves and Flows with Vorticity in Three Dimensions

Projects

3DWATERWAVES: Mathematical aspects of three-dimensional water waves with vorticity

Cite this