Hisashi Okamoto's publications

Last update: 14 April, 2014

Research Papers

  1. On the semi-discrete finite element approximation for the nonstationary Stokes equation, J. Fac. Sci. Univ. Tokyo, Sec. IA, vol. 29 (1982), pp. 241--260.
  2. On the semi-discrete finite element approximation for the nonstationary Navier-Stokes equation, J. Fac. Sci. Univ. Tokyo, Sec. IA, vol. 29 (1982), pp. 613--652.
  3. On the equation of motion of stratified fluid motion: Uniqueness and existence of the solutions, J. Fac. Sci. Univ. Tokyo, Sec. IA, vol. 30 (1984), pp. 615--643.
  4. A stationary free boundary problem for a circular flow with or without surface tension, Proc. Japan Acad. Ser. A, vol. 58 (1982), 422--424.
  5. Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension, Math. Meth. Appl. Sci., vol. 6 (1984), pp. 215--233.
  6. A generalization of Liapunov's theorem concerning a mass of fluid with self-gravitation Proc. Japan Acad. Ser. A, vol. 60 (1984), pp. 4--7.
  7. (with H. Fujita and M. Shoji), A numerical approach to a free boundary problem of a circulating perfect fluid, Japan J. Appl. Math., vol. 2 (1985), pp. 197--210.
  8. Nonstationary free boundary problem for perfect fluid with surface tension, J. Math. Soc. Japan, vol. 38 (1986), pp. 381--401.
  9. (with Y. Kimura), Vortex motion on a sphere, J. Phys. Soc. Japan, vol. 56 (1987), pp. 4203--4206.
  10. Applications of the Fourier transform to the boundary element method, J. Fac. Sci., Univ. of Tokyo, Sect. IA, vol. 35 (1988), pp. 345--362.
  11. (with M. Katsurada), A mathematical study of the charge simulation method I, J. Fac. Sci., Univ. of Tokyo, Sect. IA, vol. 35 (1988), pp. 507--518.
  12.  O(2)-equivariant Bifurcation equations of mode (1,2), Sci. Papers of Coll. Arts and Sci., Univ. Tokyo, vol. 39 (1989), pp. 1--43.
  13. On the problem of water waves of permanent configuration, Nonlinear Anal., Theory, Meth. and Appl., vol. 14 (1990), pp. 469--481.
  14. (with S.J. Tavener), Degenerate O(2)-equivariant bifurcation equations and their application to the Taylor problem, Japan J. Indust. Appl. Math., vol. 8 (1991), pp. 245--273.
  15. An algorithm for computing a nondegenerate hysteresis point, Publ. R.I.M.S., vol. 27 (1991), pp. 837--843.
  16. A uniqueness theorem for the unbounded classical solution of the nonstationary Navier-Stokes equations in R^3, J. Math. Anal. Appl., vol. 181 (1994), pp. 473--482.
  17. (with M. Shoji), Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D Tori, Japan J. Indus. Appl. Math., vol. 10 (1993), pp. 191--218.
  18. A variational problem arising in the two dimensional Navier-Stokes equations with vanishing viscosity, Appl. Math. Lett., vol. 7 (1994), pp. 29--33.
  19. (with M. Shoji), Remarks on the bifurcation of progressive waves of finite depth, Publ. R.I.M.S., vol. 30 (1994), pp. 611--640.
  20. ( with and M. Shoji ), Two Dimensional, Periodic, Capillary-Gravity Waves With Negative Surface Tension, Proc. IUTAM Conf. Structure and Dynamics of Nonlinbear Waves in Fluids, Eds. K. Kirchg\"assner and A. Mielke, World Scientific, (1995), pp. 363--369.
  21. Axisymmetric stagnation flow converging obliquely on a cylinder, J. Phys. Soc. Japan, vol. 64 (1995), pp. 2714--2717.
  22. (with M. Katsurada), On the collocation points of the fundamental solution method for the potential problem, Int. J. Comp. Math. Appl., vol. 31 (1996), pp. 123--137.
  23. (with M. Shoji), Secondary and tertiary bifurcations of capillary gravity waves, Adv. Math. Sci. Appl., vol. 6 (1996), pp. 135--145.
  24. (with T. Sakajo), Numerical computation of vortex sheet roll-up in the background shear flow, Fluid Dynam. Res., vol. 17 (1996), pp. 195--212.
  25. (with M. Shoji), The resonance of modes in the problem of capillary gravity waves, Physica D, vol. 95 (1996) pp. 336--350.
  26. Nearly singular two-dimensional Kolmogorov flows for large Reynolds number, J. Dynamics and Diff. Eqns., vol. 8 (1996), pp. 203--220.
  27. Interfacial progressive water waves: a singularity theoretic view, Tohoku Math. J. vol. 49 (1997), pp. 33--57.
  28. Exact solutions of the Navier-Stokes equations via Leray's method, Japan J. Indus. Appl. Math., , vol. 14 (1997), pp. 169--197.
  29. (with H. Fujita and H. Moriomoto), Stability analysis of Navier-Stokes flows in annuli, Math. Meth. Appl. Sci., vol. 20 (1997), pp. 959--978.
  30. (with T. Sakajo), An application of Draghicescu's fast summation method to vortex sheet motion, J. Phys. Soc. Japan, vol. 67 (1998), pp. 462--470.
  31. A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit, Proc. Int. Congress Math., vol. III, (1998), pp. 523-532.
  32. (with J. Zhu) Some similarity solutions of the Navier-Stokes equations and related topics, Taiwanese J. Math., vol. 4 (2000), pp. 65--103, ps file, 1.05 MB after gziped. Downloadable at Taiwanese J. Math.
  33. ( with X. Chen) Global Existence of Solutions to the Proudman--Johnson Equation, Proc. Japan Acad., vol. 76 (2000), pp. 149--152. 324KB
  34. (with H. Ikeda and M. Mimura) A singular perturbation problem arising in Oseen's spiral flows, Japan J. Indust. Appl. Math., vol. 18 (2001), pp. 393--403. ps file, ( 343KB after gzip ).
  35. Craik, A.D.D., Okamoto, H. \& Allen, H.R., Second-Harmonic Resonance with Parametric Excitation and Damping, in ``Fluid Mechanics and the Environment: Dynamical Approaches". Lecture Notes in Physics \# 566, ed. J.L. Lumley. Springer Verlag, (2001), pp. 63--89.
  36. (with M. Nagayama) On the interior layer appearing in the similarity solutions of the Navier-Stokes equations (622KB after gzip ) Japan J. Indust. Appl. Math., vol. 19 (2002), pp. 277--300.
  37. (with A. D. D. Craik) A three-dimensional autonomous system with unbounded `bending' solutions, Physica D, vol. 164, (2002), pp. 168--186
  38. (with M. Nagayama and J. Zhu) On the blow-up of some similarity solutions of the Navier-Stokes equations, pdf file 584KB. Quader. di Mat. vol. 10 (2003), pp. 137--162.
  39. Xinfu Chen and H. Okamoto, Global Existence of Solutions to the generalized Proudman--Johnson Equation, Proc. Japan Acad., vol. 78 (2002), pp. 136--139.
  40. K. Kobayashi, H. Okamoto, and J. Zhu, Numerical computation of water and solitary waves by the double exponential transform, J. Comp. Appl. Math., vol. 152 (2003), pp. 229--241.
  41. S.-C. Kim and H. Okamoto, Bifurcations and inviscid limit of rhombic Navier-Stokes flows in tori, IMA J. Appl. Math., vol. 68 (2003), 119--134.
  42. Xinfu Chen and H. Okamoto, A Blow-up problem modified from similarity solutions of the Euler equations, J. Math. Sci., Univ. Tokyo, vol. 10 (2003), pp373--389
  43. H. Ikeda, K. Kondo, H. Okamoto and S. Yotsutani, On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows, Commun. Pure Appl. Anal. , vol. 2 (2003) 373--382.
  44. K.-I. Nakamura, H. Okamoto, H. Yagisita, Blow-up solutions appearing in the vorticity dynamics with linear strain, J. Math. Fluid Mech., vol. 6 (2004), pp. 157--168. Downloadable at Springerlink
  45. Uniqueness of Crapper's pure capillary waves of permanent shape, pdf file J. Math. Sci., Univ. Tokyo., vol. 12 (2005), 67--75.
  46. A remark on continuous, nowhere differentiable functions, Proc. Japan Acad., vol. 81 (2005), 47--50.
  47. (with K. Ohkitani), On the role of the convection term in the equations of motion of incompressible fluid, J. Phys. Soc. Japan, vol. 74 (2005), 2737--2742.
  48. (with Sun-Chul Kim), Uniqueness of the exact solutions of the Navier-Stokes equations having null nonlinearity, Proc. R. Soc. Edinburgh, vol. 136 A (2006), 1303--1315.
  49. C.-H. Cho, S. Hamada, and H. Okamoto, On the finite difference approximation for a parabolic blow-up problem, Japan J. Indut. Appl. Math., vol. 24 (2007), 131--160.
  50. H. Okamoto and M. Wunsch, A geometric construction of continuous, strictly increasing singular functions, Proc. Japan Acad., Ser. A, vol. 83 (2007) 114--118.
  51. C.-H. Cho and H. Okamoto, Further remarks on asymptotic behavior of the numerical solutions of parabolic blow-up problem, Meth. Appl. Anal., vol. 14 (2007), 213--226.
  52. H. Okamoto, T. Sakajo, and M. Wunsch, On a generalization of the Constantin-Lax-Majda equation, Nonlinearity, VOL. 21 (2008) 2447--2461.
  53. H. Okamoto, Well-posedness of the generalized Proudman-Johnson equation without viscosity, J. Math. Fluid Mech. vol. 11 (2009), 46--59.
  54. Mayumi Shoji, Hisashi Okamoto and Takuya Ooura, Particle trajectories around a running cylinder or a sphere, Fluid Dynamics Research vol. 42 (2010), 025506(10pp).
  55. Sun-Chul Kim and Hisashi Okamoto, Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers, Japan J. Indust. Appl. Math., vol. 27 (2010), 47--71.
  56. S.-C. Kim and H. Okamoto, The generalized Proudman-Johnson equation at large Reynolds numbers, IMA J. Appl. Math., 78 (2013), 379--403.
  57. H. Okamoto and M. Shoji, Trajectories of fluid particles in a periodic water-wave, Philos. Trans. R. Soc. A vol. 370, (2012), 1661--1676.
  58. H. Okamoto, Blow-up problems in the strained vorticity dynamics and critical exponents, J. Math. Soc. Japan., vol. 65, (2013), 1079--1099,
  59. H. Okamoto, T. Sakajo, M. Wunsch, Steady-States and Traveling wave solutions of the generalized Constantin-Lax-Majda equation, Discrete and Continuus Dynamical Systems, vol. 34, (2014), 3155--3170
  60. The generalized Proudman--Johnson equation and its singular perturbation problems, online, Japan J. Indust. Appl. Math.,


Proceedings and others

1.     Stationary free boundary problems for circular flows with or without surface tension, in '' Nonlinear PDE in Appl. Sci., US-Japan Seminar, Tokyo, eds., H. Fujita, P. Lax and G. Strang, (1983), pp. 233--251.

  1. Nonstationary or stationary free boundary problems for perfect fluid with surface tension, Recent Topics in Nonlinear PDE, Hiroshima, Lecture Notes in Num. Appl. Anal., vol. 6, eds., M. Mimura and T. Nishida, (1984), pp. 143--154.
  2. Global existence theorems on nonstationary stratified flow of incompressible viscous fluid, in ``Computing Methods in Applied Sciences and Engineering, VI'', eds. R. Glowinski and J.-L. Lions, (1984), pp. 441--449.
  3. (with M. Shoji), Dynamical system arising in nonstationary motion of a free boundary of a perfect fluid, Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku, vol. 559 (1985), pp. 19--40.
  4. (with M. Shoji), On the existence of progressive waves in the flow of perfect fluid around a circle, Patterns and Waves, eds., T. Nishida, M. Mimura and H. Fujii, (1986), pp. 631--644.
  5. Degenerate bifurcations in the Taylor-Couette problem, in '' Recent Topics in Nonlinear PDE IV '', M. Miura and T. Nishida, Kinokuniya \& North Holland, (1989 ), pp. 121--128.
  6. (with Y. Kimura), Chaotic Advection by a point Vortex in a semidisk, in '' Topological Fluid Dynamics '', eds. H.K. Moffatt and A. Tsinober, Cambridge Univ. Press (1990), pp. 105--113.
  7. Applications of degenerate bifurcation equations to the Taylor problem and the water wave problem, in '' The Navier-Stokes Equations Theory and Numerical Method '', eds. J.G. Heywood, K. Masuda, R. Rautmann and V.A. Solonnikov, Springer Lecture Notes in Math., No. 1431 (1990), pp. 117--127.
  8. (with M. Shoji), Normal forms of bifurcation equations in the problem of capillary-gravity waves, Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku, vol. 740 (1991), pp. 208--242.
  9. (with M. Shoji), Nonexistence of bifurcation from Crapper's pure capillary waves, Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku, vol. 745 (1991), 21--38.
  10. (with M. Shoji), The Stokes expansion method to the bifurcation problem of plane progressive water waves, Nonlinear PDE, Lecture Notes in Num. Appl. Anal., vol. 11, eds., M. Mimura and T. Nishida, (1991), pp. 137--152.
  11. (with M. Shoji and M. Katsurada), A computer-assisted analysis of the two dimensional Navier-Stokes equations, in Proceedings of the Functional Analysis and Related Topics, 1991 ( ed. H. Komatsu ), Springer Lecture Note in Math. vol. 1540 (1993), pp. 309--318.
  12. (with M. Shoji), Numerical unfoldings of capillary gravity waves, in Proceedings of the First China-Japan Seminar on Numerical Mathematics, eds. Z.-c. Shi and T. Ushijima, World Scientific, (1993), pp. 119--132.
  13. (with M. Katsurada and M. Shoji), Bifurcation of the stationary Navier- Stoke flows on a 2-D Torus, to appear in Proc. Katata Workshop on Nonlinear PDEs. and Applications, eds. M. Mimura and T. Nishida.
  14. Singular or nearly singular flows of incompressible fluid, International Institute for Advanced Study, IIAS Report No. 1996-003, ed. T. Miwa, pp. 11--30.
  15. H. Fujita, H. Moriomoto, and H. Okamoto, Stability of some Navier-Stokes flows in doubly connected domains, in ``Recent Development in Domain Decomposition Methods and Flow Problems'', eds. H. Fujita et al., Gakuto International Series, Math. Sci. Appl., vol. 11 (1998), pp. 116--125. PS file, 80KB after gzip
  16. H. Okamoto and M Shoji, Boundary layer in unsteady two-dimensional Navier-Stokes equations, ibid, pp. 171--180.
  17. Localization of singularities in inviscid limit --- numerical examples, in Proceedings of Navier-Stokes equations: theory and numerical methods, ed. R. Salvi, Longman, Pitman Research Notes in Mathematics Series vol. 388 (1998), pp. 220--236. PS file, 828KB after gzip
  18. K. Ohkitani and H. Okamoto, Blow-up problems modeled from the strain-vorticity dynamics, Proceedings of ``Tosio Kato's method and Principle for Evolution Equations in Mathematical Physics" ( = RIMS Kokyuroku # 1234 ), (2001), pp. 240--250.
  19. K. Kobayashi and H. Okamoto, Uniqueness issues on permanent progressive water-waves, Proc. of ``Nonlinear Waves'' held at Oberwolfach in January 2004. J. Nonlinear Math. Phys., vol. 11, 472--479.
  20. (with C.-H. Cho, S. Hamada) On the finite difference approximation for parabolic blow-up problems, in ``Proc. 7th China-Japan Seminar on Numerical Mathematics'', eds. Z.-c. Shi and H. Okamoto, Sciecne Press Beijing, (2006), pp 193--202.
  21. A nonlinear boundary-value problem with an integral constraint, in Proceedings of ``Far-From-Equilibrium Dynamics'', RIMS Kokyuroku Bessatsu, B31 (2012), 93--115. (refereed paper)


Textbook on progressive water-waves

( with M. Shoji ) The Mathematical Theory of Bifurcation of Permanent Progressive Water-Waves, World Scientific, 2001.

Contents in postscript file

Cover of the book

Reviewed by Zentralblatt

Reviewed by J. Fluid Mech.



Publications in Japanese

  1. 岡本 久、R. Finn 教授講演記録、数学、第33巻(1981), p84.
  2. 岡本 久, 完全流体の自由境界問題--- 分岐解とその安定性, 数学vol. 38 (1986), pp. 39--52.
  3. 岡本 久, 桂田 祐史, ポテンシャル問題の高速解法について, 応用数理, 第二巻 第三号(1992), pp. 2--20.
  4. 岡本 久, 定常表面張力波について, ながれ, vol. 13 (1994), pp. 184--195.
  5. 藤井 宏、岡本 久, 非線型力学, 岩波書店 岩波講座「応用数学」(1995, 改定版(1998).
  6. 岡本 久、流れの解析、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
  7. 岡本 久, 中村 周, 関数解析, 岩波書店 岩波講座「現代数学の基礎」(1997. 新装版(2006).
  8. 岡本 久、数値解析と応用数学関連の報告、数学、第51(1999), p210--212.
  9. 岡本 久, Navier-Stokes 方程式の解の構造, ながれ, vol. 19 (2000), pp. 172--179.
  10. 岡本 久, Navier-Stokes 方程式の未解決問題, 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
  11. 岡本 久, 水面波の多様性, 数学のたのしみ, 2001年6月号, pp. 62--70.
  12. 岡本 久, Proudmann-Johnson方程式の周辺の話題, 数理解析研究所講究録, 1225, (2001), pp. 176-179.
  13. Kim Sun-Chul & 岡本 久, 菱形Navier-Stokes流の解の分岐と非粘性極限, 数理解析研究所講究録, 1231, (2001), pp. 69-82.
  14. (10名による共著), 数学七つの未解決問題,, 森北出版, (2002). 第7章が岡本と藤田宏による共同解説。
  15. 現象の数理, 放送大学教材(2003年、3月刊行, 一般の書店でも購入できます)
  16. 岡本 久、中村健一、柳下浩紀、Navier-Stokes 方程式の非有解な解は爆発し得る, 数理解析研究所講究録1322(2003), 102--106 PS file , PDF file
  17. 岡本 久, 知られざるグリーン, 数学セミナー2003年7月号, 45--49.
  18. 岡本 久、 計算機実験と数学 変わり者の独り言、土木学会誌、vol. 882003年 8月号、32ページ. HTML
  19. (翻訳) ピーターD. ラックス、数学と数値計算、「数学の最先端」第4巻、アーノルド他編、砂田利一監訳、(2003) pp 26--47.
  20. 岡本 久、 応用解析等教科書の個人的な概観、応用数理、第14巻(2004), 97--101.
  21. 岡本 久, Crapperの表面張力波の一意性について, 数理解析研究所講究録, 1368, (2004), pp. 136-143.
  22. 数学とコンピュータ(4名による共著), 放送大学教材(2006年、4月刊,253pages)
  23. ニュートン法の話、「数学のたのしみ」2006年春号、70--91.
  24. ルレイと非線形編微分方程式、数学セミナー、45巻 No. 12 (2006), 24--29.
  25. ソウル大学数学教室訪問記、数学セミナー、46巻 No. 6 (2006), 44--47.
  26. ナヴィエ-ストークス方程式の導き方, 「数理科学」、201011月号、71--77.
  27. ある応用数学者の弁明、数学の道しるべ、サイエンス社 (2011), 112--121.
  28. 流体力学の厳密解、「数理科学」201211月号、
  29. 流体力学と数学、「数学通信」, 18巻 第2 (2013),  6-12.
  30. 最近の乱流理論、筑摩学芸文庫「数理物理学の方法」にフォン・ノイマンの論文を山田道夫氏と邦訳しました。2013年。

  1. ナヴィエ・ストークス方程式の数理, 東京大学出版会、2009年 6月
  2. 関数概念の発展、長岡亮介氏との共著、近代科学社