Existence proof of unimodal solutions of the Proudman–Johnson equation via interval analysis View Full Text


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Article Info

DATE

2019-01

AUTHORS

Tomoyuki Miyaji, Hisashi Okamoto

ABSTRACT

The Proudman–Johnson equation is considered as a representative of the two-dimensional fluid flow. Its steady-states are computed and their existence and unimodality are proved rigorously via the interval analysis and the interval Newton method. By using both the multiple shooting method and multiple-precision arithmetic our verification succeeds up to the Reynolds number ≤5000. More... »

PAGES

1-12

References to SciGraph publications

  • 2010-06. Vortices of large scale appearing in the 2D stationary Navier–Stokes equations at large Reynolds numbers in JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
  • 2002-10. C1 Lohner Algorithm in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 2018-04-06. Models and Special Solutions of the Navier-Stokes Equations in HANDBOOK OF MATHEMATICAL ANALYSIS IN MECHANICS OF VISCOUS FLUIDS
  • 2016. Models and Special Solutions of the Navier–Stokes Equations in HANDBOOK OF MATHEMATICAL ANALYSIS IN MECHANICS OF VISCOUS FLUIDS
  • 1985-06. Multiple shooting using interval analysis in BIT NUMERICAL MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s13160-018-00339-x

    DOI

    http://dx.doi.org/10.1007/s13160-018-00339-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1111058708


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