Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Reference32 articles.
1. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series, vol. 55. Dover Publications, New York (1983)
2. Acevedo, P., Amrouche, C., Conca, C., Ghosh, A.: Stokes and Navier–Stokes equations with Navier boundary condition. C. R. Math. Acad. Sci. Paris 357, 115–119 (2019)
3. Ada Reference Manual, ISO/IEC 8652:2012(E)
4. Amrouche, C., Rejaiba, A.: $$L^p$$-theory for Stokes and Navier–Stokes equations with Navier boundary condition. J. Differ. Equ. 256, 1515–1547 (2014)
5. Arioli, G., Gazzola, F., Koch, H.: Programs and data files for the proof of Lemmas 2, 3 and 5. http://www1.mate.polimi.it/gianni/sns.tgz
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