A computer-assisted proof on the stability of the Kolmogorov flows of incompressible viscous fluid

DOI10.1016/j.cam.2003.10.016zbMath1058.76028OpenAlexW2001029445MaRDI QIDQ1877193

Kaori Nagatou

Publication date: 16 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.10.016

zbMATH Keywords

infinite-dimensional eigenvalue problems

Mathematics Subject Classification ID

Related Items (9)

An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid ⋮ Improvement of infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem ⋮ A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid ⋮ Numerical verification method for infinite dimensional eigenvalue problems ⋮ Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers ⋮ Numerical verification for solutions to partial differential equations ⋮ Kolmogorov flow: Linear stability and energy transfers in a minimal low-dimensional model ⋮ Applicability of the interval Taylor model to the computational proof of existence of periodic trajectories in systems of ordinary differential equations ⋮ A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations

Uses Software

• PROFIL/BIAS

Cites Work

• Unnamed Item
• Numerical verifications of solutions for nonlinear elliptic equations
• Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori
• PROFIL/BIAS - A fast interval library
• A numerical method to verify the elliptic eigenvalue problems including a uniqueness property
• Bifurcation analysis of Kolmogorov flows
• Numerical verifications for eigenvalues of second-order elliptic operators
• Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid
• Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid

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