Uniqueness and Bifurcation Branches for Planar Steady Navier–Stokes Equations Under Navier Boundary Conditions

The stationary Navier–Stokes equations under Navier boundary conditions are considered in a square. The uniqueness of solutions is studied in dependence of the Reynolds number and of the strength of the external force. For some particular forcing, it is shown that uniqueness persists on some continu...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 23; no. 3
Main Authors Arioli, Gianni, Gazzola, Filippo, Koch, Hans
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2021
Springer Nature B.V
Subjects
Bifurcations
Boundary conditions
Classical and Continuum Physics
Computational fluid dynamics
Fluid flow
Fluid mechanics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Navier-Stokes equations
Physics
Physics and Astronomy
Reynolds number
Theoretical mathematics
Uniqueness
Navier–Stokes equations
Navier boundary conditions
74G35
Computer assisted proof
Uniquenes
Bifurcation
35Q30
37M20
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Summary:The stationary Navier–Stokes equations under Navier boundary conditions are considered in a square. The uniqueness of solutions is studied in dependence of the Reynolds number and of the strength of the external force. For some particular forcing, it is shown that uniqueness persists on some continuous branch of solutions, when these quantities become arbitrarily large. On the other hand, for a different forcing, a branch of symmetric solutions is shown to bifurcate, giving rise to a secondary branch of nonsymmetric solutions. This proof is computer-assisted, based on a local representation of branches as analytic arcs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-021-00572-4