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

• Published in: Journal of mathematical fluid mechanics Vol. 23; no. 3
• Main Authors: Arioli, Gianni, Gazzola, Filippo, Koch, Hans
• Format: Journal Article
• Language: English
• 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

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...