Steady threedimensional rotational flows : An approach via two stream functions and NashMoser iteration
(2019) In Analysis and PDE 12(5). p.12251258 Abstract
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) × ℝ^{2}. 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) × ℝ^{2}. 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 NashMoser 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 threedimensional 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, NashMoser iteration method, Vorticity
 in
 Analysis and PDE
 volume
 12
 issue
 5
 pages
 34 pages
 publisher
 Mathematical Sciences Publishers
 external identifiers

 scopus:85058886417
 ISSN
 21575045
 DOI
 10.2140/apde.2019.12.1225
 language
 English
 LU publication?
 yes
 id
 20ec175ab5bc48bdb4ffa33704a9408a
 date added to LUP
 20190102 14:43:27
 date last changed
 20190220 11:41:14
@article{20ec175ab5bc48bdb4ffa33704a9408a, 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 NashMoser 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 threedimensional flows with nonvanishing vorticity.</p>}, author = {Buffoni, Boris and Wahlén, Erik}, issn = {21575045}, keyword = {Boundary conditions,Incompressible flows,NashMoser iteration method,Vorticity}, language = {eng}, number = {5}, pages = {12251258}, publisher = {Mathematical Sciences Publishers}, series = {Analysis and PDE}, title = {Steady threedimensional rotational flows : An approach via two stream functions and NashMoser iteration}, url = {http://dx.doi.org/10.2140/apde.2019.12.1225}, volume = {12}, year = {2019}, }