Steady three-dimensional rotational flows : An approach via two stream functions and Nash-Moser iteration
Buffoni, Boris and Wahlén, Erik LU
(2019)
In Analysis and PDE
12(5).
p.1225-1258
- Abstract
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) × ℝ2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of the boundary ∂D. The Bernoulli equation states that the "Bernoulli function" H := 1/2 |v|2 + p (where v is the velocity field and p the pressure) is constant along stream lines, that is, each particle is associated with a particular value of H. We also prescribe the value of H on ∂D. The aim of this work is to develop an existence theory near a given constant solution. It relies on writing the velocity field in the form v = ∇ f × ∇g and deriving a degenerate... (More)
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) × ℝ2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of the boundary ∂D. The Bernoulli equation states that the "Bernoulli function" H := 1/2 |v|2 + p (where v is the velocity field and p the pressure) is constant along stream lines, that is, each particle is associated with a particular value of H. We also prescribe the value of H on ∂D. The aim of this work is to develop an existence theory near a given constant solution. It relies on writing the velocity field in the form v = ∇ f × ∇g and deriving a degenerate nonlinear elliptic system for f and g. This system is solved using the Nash-Moser method, as developed for the problem of isometric embeddings of Riemannian manifolds; see, e.g., the book by Q. Han and J.-X. Hong (2006). Since we can allow H to be nonconstant on ∂D, our theory includes three-dimensional flows with nonvanishing vorticity.
(Less)
- author
- Buffoni, Boris
and Wahlén, Erik
LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Boundary conditions, Incompressible flows, Nash-Moser iteration method, Vorticity
- in
- Analysis and PDE
- volume
- 12
- issue
- 5
- pages
- 34 pages
- publisher
- Mathematical Sciences Publishers
- external identifiers
-
- scopus:85058886417
- ISSN
- 2157-5045
- DOI
- 10.2140/apde.2019.12.1225
- project
- Mathematical aspects of three-dimensional water waves with vorticity
- language
- English
- LU publication?
- yes
- id
- 20ec175a-b5bc-48bd-b4ff-a33704a9408a
- date added to LUP
- 2019-01-02 14:43:27
- date last changed
- 2024-10-01 13:41:30
@article{20ec175a-b5bc-48bd-b4ff-a33704a9408a,
abstract = {{<p>We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) × ℝ<sup>2</sup>. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of the boundary ∂D. The Bernoulli equation states that the "Bernoulli function" H := 1/2 |v|<sup>2</sup> + p (where v is the velocity field and p the pressure) is constant along stream lines, that is, each particle is associated with a particular value of H. We also prescribe the value of H on ∂D. The aim of this work is to develop an existence theory near a given constant solution. It relies on writing the velocity field in the form v = ∇ f × ∇g and deriving a degenerate nonlinear elliptic system for f and g. This system is solved using the Nash-Moser method, as developed for the problem of isometric embeddings of Riemannian manifolds; see, e.g., the book by Q. Han and J.-X. Hong (2006). Since we can allow H to be nonconstant on ∂D, our theory includes three-dimensional flows with nonvanishing vorticity.</p>}},
author = {{Buffoni, Boris and Wahlén, Erik}},
issn = {{2157-5045}},
keywords = {{Boundary conditions; Incompressible flows; Nash-Moser iteration method; Vorticity}},
language = {{eng}},
number = {{5}},
pages = {{1225--1258}},
publisher = {{Mathematical Sciences Publishers}},
series = {{Analysis and PDE}},
title = {{Steady three-dimensional rotational flows : An approach via two stream functions and Nash-Moser iteration}},
url = {{http://dx.doi.org/10.2140/apde.2019.12.1225}},
doi = {{10.2140/apde.2019.12.1225}},
volume = {{12}},
year = {{2019}},
}