計算機実験と数学変わり者の独り言

岡本久

土木学会誌、vol. 88、2003年８月号、３２ページ, 2003
Navier-Stokes 方程式の非有解な解は爆発し得る

岡本久, 中村健一, 柳下浩紀

数理解析研究所講究録, 1322 102-106, 2003
A Blow-up problem modified from similarity solutions of the Euler equations

Xinfu Chen, H. Okamoto

J. Math. Sci., Univ. Tokyo, 10 373-389, 2003 Peer-reviewed
On the blow-up of some similarity solutions of the Navier-Stokes equations

H. Okamoto, M. Nagayama, J. Zhu

Quader. di Mat., 10 137-162, 2003 Peer-reviewed
Global existence of solutions to the generalized Proudman-Johnson equation

XF Chen, H Okamoto

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 78(7) 136-139, Sep, 2002 Peer-reviewed
A three-dimensional autonomous system with unbounded 'bending' solutions

ADD Craik, H Okamoto

PHYSICA D-NONLINEAR PHENOMENA, 164(3-4) 168-186, Apr, 2002 Peer-reviewed
On the Interior Layer Appearing in the Similarity Solutions of the Navier-Stokes Equations

M. Nagayama, H. Okamoto

Japan Journal of Industrial and Applied Mathematics, 19(2) 277-300, 2002 Peer-reviewed
A singular perturbation problem arising in Oseen's spiral flows

H Ikeda, M Mimura, H Okamoto

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 18(2) 393-403, Jun, 2001 Peer-reviewed
菱形Navier-Stokes流の解の分岐と非粘性極限

Kim Sun-Chul, 岡本久

数理解析研究所講究録, 1231 69-82, 2001
Proudmann-Johnson方程式の周辺の話題

岡本久

数理解析研究所講究録, 1225 176-179, 2001
水面波の多様性

岡本久

数学のたのしみ 2001年6月号, (25) 62-70, 2001
Navier-Stokes 方程式の未解決問題

岡本久

数理科学 2001年５月号, pp. 67--74. 上野健爾・高橋陽一郎・中島啓共編、「数学の未解決問題、２１世紀数学への序章」、サイエンス社2003年、152--160 に再録, 39(5) 67-74, 2001
Blow-up problems modeled from the strain-vorticity dynamics

K. Ohkitani, H. Okamoto

Proceedings of ``Tosio Kato's method and Principle for Evolution Equations in Mathematical Physics" RIMS Kokyuroku, 1234 240-250, 2001
The Mathematical Theory of Bifurcation of Permanent Progressive Water-Waves

H. Okamoto, M. Shoji

World Scientific, 2001 Peer-reviewed
Second-harmonic resonance with parametric excitation and damping

ADD Craik, H Okamoto, HR Allen

FLUID MECHANICS AND THE ENVIRONMENT: DYNAMICAL APPROACHES, 566 63-89, 2001 Peer-reviewed
Some similarity solutions of the Navier-Stokes equations and related topics

H Okamoto, JH Zhu

TAIWANESE JOURNAL OF MATHEMATICS, 4(1) 65-103, Mar, 2000 Peer-reviewed
On the Structure of the Solutions to Navier-Stokes Equations

OKAMOTO Hisashi

nagare, 19(3) 172-179, 2000
Global Existence of Solutions to the Proudman--Johnson Equation

H. Okamoto, X. Chen

Proc. Japan Acad., 76 149-152, 2000 Peer-reviewed
An application of Draghicescu's fast summation method to vortex sheet motion

T Sakajo, H Okamoto

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 67(2) 462-470, Feb, 1998 Peer-reviewed
Stability of some Navier-Stokes flows in doubly connected domains, in ``Recent Development in Domain Decomposition Methods and Flow Problems''

H. Fujita, H. Moriomoto, H. Okamoto

eds. H. Fujita et al., Gakuto International Series, Math. Sci. Appl., 11 116-125, 1998
Localization of singularities in inviscid limit --- numerical examples, in Proceedings of Navier-Stokes equations: theory and numerical methods

H. Okamoto

ed. R. Salvi, Longman, Pitman Research Notes in Mathematics Series, 388 220-236, 1998
A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit

H. Okamoto

Proc. Int. Congress Math., III 523-532, 1998 Peer-reviewed
Stability analysis of Navier-Stokes flows in annuli

H Fujita, H Morimoto, H Okamoto

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 20(11) 959-978, Jul, 1997 Peer-reviewed
Interfacial progressive water waves - A singularity-theoretic view

H Okamoto

TOHOKU MATHEMATICAL JOURNAL, 49(1) 33-57, Mar, 1997 Peer-reviewed
Exact solutions of the navier-stokes equations via Leray's scheme

Hisashi Okamoto

Japan Journal of Industrial and Applied Mathematics, 14(2) 169-197, 1997 Peer-reviewed
Numerical computation of vortex sheet roll-up in the background shear flow

T Sakajo, H Okamoto

FLUID DYNAMICS RESEARCH, 17(4) 195-212, Mar, 1996 Peer-reviewed
流れの解析

岡本久

数理科学１９９６年５月号、pp. 64--70. 別冊・数理科学、「微積分の広がり、その魅力と多様な進化」、2004年、162--168 に再録, 64-70, 1996
Nearly singular two-dimensional Kolmogorov flows for large Reynolds numbers

Hisashi Okamoto

Journal of Dynamics and Differential Equations, 8(2) 203-220, 1996 Peer-reviewed
The resonance of modes in the problem of two-dimensional capillary-gravity waves

Hisashi Okamoto, Mayumi Shoji

Physica D: Nonlinear Phenomena, 95(3-4) 336-350, 1996 Peer-reviewed
Secondary and tertiary bifurcations of capillary gravity waves

H. Okamoto, M. Shoji

Adv. Math. Sci. Appl., 6 135-145, 1996 Peer-reviewed
The collocation points of the fundamental solution method for the potential problem.

M Katsurada, H Okamoto

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 31(1) 123-137, Jan, 1996 Peer-reviewed
AXISYMMETRICAL STAGNATION FLOW CONVERGING OBLIQUELY ON A CYLINDER

H OKAMOTO

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 64(8) 2714-2717, Aug, 1995 Peer-reviewed
Two Dimensional, Periodic, Capillary-Gravity Waves With Negative Surface Tension in Fluids

H. Okamoto, M. Shoji

World Scientific, 363-369, 1995 Peer-reviewed
REMARKS ON THE BIFURCATION OF 2-DIMENSIONAL CAPILLARY-GRAVITY WAVES OF FINITE DEPTH

H OKAMOTO, M SHOJI

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 30(4) 611-640, Dec, 1994 Peer-reviewed
定常表面張力波について

岡本久

ながれ, 13 184-195, 1994
Remarks on the Bifurcation of Two Dimensional Capillary-Gravity Waves of Finite Depth∗

Hisashi Okamoto, Mayumi Shöji, Mayumi Shöji

Publications of the Research Institute for Mathematical Sciences, 30(4) 611-640, 1994 Peer-reviewed
A VARIATIONAL PROBLEM ARISING IN THE 2-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH VANISHING VISCOSITY

H OKAMOTO

APPLIED MATHEMATICS LETTERS, 7(1) 29-33, Jan, 1994 Peer-reviewed
A UNIQUENESS THEOREM FOR THE UNBOUNDED CLASSICAL SOLUTION OF THE NONSTATIONARY NAVIER-STOKES EQUATIONS IN R(3)

H OKAMOTO

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 181(2) 473-482, Jan, 1994 Peer-reviewed
Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori

H. Okamoto, M. Shoji

Japan Journal of Industrial and Applied Mathematics, 10(2) 191-218, Jun, 1993 Peer-reviewed
A computer-assisted analysis of the two dimensional Navier-Stokes equations, in Proceedings of the Functional Analysis and Related Topics, 1991

H. Okamoto, M. Shoji

( ed. H. Komatsu ), Springer Lecture Note in Math., 1540 309-318, 1993
Numerical unfoldings of capillary gravity waves, in Proceedings of the First China-Japan Seminar on Numerical Mathematics

H. Okamoto, M. Shoji

eds. Z.-c. Shi and T. Ushijima, World Scientific, 119-132, 1993
A Rapid Solver for the Potential Problems

Okamoto Hisashi, Katsurada Masashi

Bulletin of the Japan Society for Industrial and Applied Mathematics, 2(3) 212-230, 1992

The linear potential problem not only arises as it is but also appears as a part of nonlinear problem solvers. Hence a rapid solver for the potential problem is of considerable value. Although so many good computer programs are available now, it is worthwhile using programs according as their specific aims rather than solving both complicated problems and simple problems like the potential ones in a single computer code. In this paper we attempt to survey recent results on some algorithms which work only for the Laplace operator but is rapid.
ポテンシャル問題の高速解法について

岡本久, 桂田祐史

応用数理, 2(3) 2-20, 1992 Peer-reviewed
Degenerate O(2)-Equivariant bifurcation equations and their applications to the taylor problem

Hisashi Okamoto, Simon J. Tavener

Japan Journal of Industrial and Applied Mathematics, 8(2) 245-273, Jun, 1991 Peer-reviewed
An Algorithm for Computing a Nondegenerate Hysteresis Point

Hisashi Okamoto

Publications of the Research Institute for Mathematical Sciences, 27(6) 945-952, 1991 Peer-reviewed
The Stokes expansion method to the bifurcation problem of plane progressive water waves, Nonlinear PDE, Lecture Notes

H. Okamoto, M. Shoji

Num. Appl. Anal. eds., M. Mimura and T. Nishida,, 11 137-152, 1991
Normal forms of bifurcation equations in the problem of capillary-gravity waves

H. Okamoto, M. Shoji

Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku, 740 208-242, 1991
Nonexistence of bifurcation from Crapper's pure capillary waves

H. Okamoto, M. Shoji

Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku, 745 21-38, 1991
An algorithm for computing a nondegenerate hysteresis point

H. Okamoto

Publ. R.I.M.S., 27 837-843, 1991 Peer-reviewed
ON THE PROBLEM OF WATER-WAVES OF PERMANENT CONFIGURATION

H OKAMOTO

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 14(6) 469-481, Mar, 1990 Peer-reviewed

Misc.

微分が果たす役割

岡本久

数学セミナー, 63(6) 8-14, Jun, 2024
流体力学－様々な研究者の行き交うところ

科学, 94(1) 38-41, 2024
解析学

数学セミナー, 61(4) 25-31, Apr, 2022
常微分方程式の求積

岡本久

数学セミナー, 58(6) 8-12, Jun, 2019
関数の連続性

岡本久

数学セミナー, 57(11) 8-13, Nov, 2018 Invited

Books and Other Publications

Pythonを使った数値計算入門 : 数論から円周率、分子の拡散まで

岡本, 久, 柳澤, 優香 (Role: Joint author)

近代科学社Digital,近代科学社, Mar, 2025 (ISBN: 9784764907249)
最大最小の物語 : 関数を通して自然の原理を理解する

岡本, 久

サイエンス社, Mar, 2019 (ISBN: 9784781914404)
日常現象から解析学へ

岡本久

近代科学社, Feb, 2016
関数とは何か

岡本久, 長岡亮介 (Role: Joint author)

Jul, 2014
数理物理学の方法

岡本久, 山田道夫 (Role: Joint translator, 最近の乱流理論)

Dec, 2013

Presentations

An application of interval arithmetic to certain dynamical systems arising in fluid mechanics

Hisashi Okamoto

The 9th International Conference on Computational Physics, Jan 9, 2015
Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers

Hisashi Okamoto

Colloquium, Nov 20, 2014
Topologically simple patterns appearing in the 2D Navier-Stokes equations at large Reynolds numbers

Hisashi Okamoto

The 8th CREST-SBM International Conference International Conference on Mathematical Fluid Dynamics, Nov 14, 2014
Trajectories of fluid particles around spheres and in a water wave

Hisashi Okamoto

Theory of Water Waves, Jul 22, 2014
Unimodal Patterns appearing in the 2D Navier-Stokes equations at large Reynolds numbers

Hisashi Okamoto

Conference of East Asia Section of SIAM, Jun 23, 2014

Professional Memberships

Research Projects

Studies on the Navier-Stokes equations by numerical methods

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2022 - Mar, 2026
非圧縮流体の力学的諸問題の数理的研究

科学研究費助成事業, 日本学術振興会, Apr, 2018 - Mar, 2022

岡本久
Optimal Operation of Irrigation Schemes Based on Viscosity Solutions of Partial Differential Equations

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Jul, 2016 - Mar, 2020

Unami Koichi
Mathematical study of micro pressure waves for developments in modern high-speed trains

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Jul, 2015 - Mar, 2020

Sakajo Takashi
Study of the dynamics and anisotropy of flow structures in turbulence by large scale numerical analysis

Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2018

Kimura Yoshifumi, KANEDA Yukio, YOSHIMATSU Katsunoni, SAKAJO Takashi, MATSUO Takayasu

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