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Uniqueness and bifurcation branches for planar steady Navier-Stokes equations under Navier boundary conditions. (English) Zbl 1468.35104

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.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35B32 Bifurcations in context of PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)

Software:

navierstokes; Ada95
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Full Text: DOI

References:

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