Existence proof of unimodal solutions of the Proudman-Johnson equation via interval analysis

DOI10.1007/s13160-018-00339-xzbMath1410.76332OpenAlexW2907868087WikidataQ128640602 ScholiaQ128640602MaRDI QIDQ1736471

Tomoyuki Miyaji, Hisashi Okamoto

Publication date: 26 March 2019

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

Full work available at URL: https://doi.org/10.1007/s13160-018-00339-x

zbMATH Keywords

interval analysiscomputer-assisted proofProudman-Johnson equationmultiple shooting methodunimodal solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Incompressible viscous fluids (76D99) Algorithms with automatic result verification (65G20)

Related Items

CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems

Uses Software

• SciPy

Cites Work

• An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid
• Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers
• Multiple shooting using interval analysis
• Some similarity solutions of the Navier-Stokes equations and related topics
• Unimodal patterns appearing in the two-dimensional Navier-Stokes flows under general forcing at large Reynolds numbers
• \(C^1\) Lohner algorithm.
• On the well-posedness of various one-dimensional model equations for fluid motion
• A computer-assisted proof of existence of a periodic solution
• A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
• Verification methods: Rigorous results using floating-point arithmetic
• Solving Ordinary Differential Equations I
• Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers
• Multiple shooting method for two-point boundary value problems
• Estimating Regions of Existence of Unstable Periodic Orbits Using Computer-Based Techniques
• The generalized Proudman-Johnson equation at large Reynolds numbers
• A Four-Leaf Chaotic Attractor of a Three-Dimensional Dynamical System
• Boundary-layer growth near a rear stagnation point

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