Hisashi Okamoto's publications
Last update: 6 December, 2013
Research Papers
- 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.
- 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.
- 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.
- A
stationary free boundary problem for a circular flow with or without
surface tension, Proc. Japan Acad. Ser. A, vol. 58 (1982), 422--424.
- Bifurcation
phenomena in a free boundary problem for a circulating flow with surface
tension, Math. Meth. Appl. Sci., vol. 6 (1984), pp. 215--233.
- 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.
- (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.
- Nonstationary free boundary
problem for perfect fluid with surface tension, J. Math. Soc. Japan, vol.
38 (1986), pp. 381--401.
- (with Y.
Kimura), Vortex motion on a sphere, J. Phys. Soc. Japan, vol. 56 (1987),
pp. 4203--4206.
- Applications
of the Fourier transform to the boundary element method, J. Fac. Sci.,
Univ. of Tokyo, Sect. IA, vol. 35 (1988), pp. 345--362.
- (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.
- O(2)-equivariant
Bifurcation equations of mode (1,2), Sci. Papers of Coll. Arts and Sci.,
Univ. Tokyo, vol. 39 (1989), pp. 1--43.
- On the
problem of water waves of permanent configuration, Nonlinear Anal.,
Theory, Meth. and Appl., vol. 14 (1990), pp. 469--481.
- (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.
- An
algorithm for computing a nondegenerate
hysteresis point, Publ. R.I.M.S., vol. 27 (1991), pp. 837--843.
- 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.
- (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.
- A variational problem arising in the two dimensional
Navier-Stokes equations with vanishing viscosity, Appl. Math. Lett., vol. 7 (1994), pp. 29--33.
- (with M.
Shoji), Remarks on the bifurcation of progressive waves of finite depth,
Publ. R.I.M.S., vol. 30 (1994), pp. 611--640.
- ( 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.
- Axisymmetric
stagnation flow converging obliquely on a cylinder, J. Phys. Soc. Japan,
vol. 64 (1995), pp. 2714--2717.
- (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.
- (with M.
Shoji), Secondary and tertiary bifurcations of capillary gravity waves,
Adv. Math. Sci. Appl., vol. 6 (1996), pp. 135--145.
- (with T.
Sakajo), Numerical computation of vortex sheet roll-up in the background shear
flow, Fluid Dynam. Res., vol. 17 (1996), pp.
195--212.
- (with M.
Shoji), The resonance of modes in the problem of capillary gravity waves, Physica D, vol. 95 (1996) pp. 336--350.
- Nearly
singular two-dimensional Kolmogorov flows for large Reynolds number, J.
Dynamics and Diff. Eqns., vol. 8 (1996), pp. 203--220.
- Interfacial
progressive water waves: a singularity theoretic view, Tohoku Math. J.
vol. 49 (1997), pp. 33--57.
- Exact
solutions of the Navier-Stokes equations via Leray's
method, Japan J. Indus. Appl. Math., , vol. 14 (1997), pp. 169--197.
- (with H.
Fujita and H. Moriomoto), Stability analysis of
Navier-Stokes flows in annuli, Math.
Meth. Appl. Sci., vol. 20 (1997), pp. 959--978.
- (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.
- A
study of bifurcation of Kolmogorov flows with an emphasis on the singular
limit, Proc. Int. Congress Math., vol. III, (1998), pp. 523-532.
- (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.
- ( with X.
Chen) Global
Existence of Solutions to the Proudman--Johnson Equation, Proc. Japan
Acad., vol. 76 (2000), pp. 149--152. 324KB
- (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
).
- 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.
- (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.
- (with A.
D. D. Craik) A three-dimensional
autonomous system with unbounded `bending' solutions, Physica D, vol. 164, (2002), pp. 168--186
- (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.
- Xinfu Chen and H. Okamoto,
Global Existence of Solutions to the generalized Proudman--Johnson
Equation, Proc. Japan Acad., vol. 78 (2002), pp. 136--139.
- 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.
- 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.
- 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
- 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.
- 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
- Uniqueness
of Crapper's pure capillary waves of permanent shape, pdf file J.
Math. Sci., Univ. Tokyo., vol. 12 (2005), 67--75.
- A
remark on continuous, nowhere differentiable functions, Proc. Japan
Acad., vol. 81 (2005), 47--50.
- (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.
- (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.
- 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.
- H. Okamoto
and M. Wunsch, A
geometric construction of continuous, strictly increasing singular
functions, Proc. Japan Acad., Ser. A, vol. 83 (2007) 114--118.
- 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.
- H.
Okamoto, T. Sakajo, and M. Wunsch, On
a generalization of the Constantin-Lax-Majda equation, Nonlinearity,
VOL. 21 (2008) 2447--2461.
- H.
Okamoto, Well-posedness
of the generalized Proudman-Johnson equation without viscosity, J.
Math. Fluid Mech. vol. 11 (2009), 46--59.
- Mayumi
Shoji, Hisashi Okamoto and Takuya Ooura, Particle trajectories around a
running cylinder or a sphere, Fluid
Dynamics Research vol. 42 (2010), 025506(10pp).
- 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.
- S.-C. Kim
and H. Okamoto, The generalized Proudman-Johnson
equation at large Reynolds numbers, IMA
J. Appl. Math., 78 (2013), 379--403.
- H. Okamoto
and M. Shoji, Trajectories of fluid particles in a periodic water-wave, Philos.
Trans. R. Soc. A vol. 370, (2012), 1661--1676.
- H.
Okamoto, Blow-up problems in the strained vorticity
dynamics and critical exponents, J. Math. Soc. Japan., vol. 65, (2013),
1079--1099,
- 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
-
The generalized Proudman--Johnson equation and its singular perturbation problems,
online in Japan J. Indust. Appl. Math.,
-
A four-leaf chaotic attractor of a three-dimensional dynamical system, accepted by International Journal of Bifurcation and Chaos
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.
- 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.
- 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.
- (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.
- (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.
- 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.
- (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.
- 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.
- (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.
- (with M.
Shoji), Nonexistence of bifurcation from Crapper's pure capillary waves,
Res. Inst. Math. Sci., Kyoto Univ., Kokyuroku,
vol. 745 (1991), 21--38.
- (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.
- (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.
- (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.
- (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.
- Singular
or nearly singular flows of incompressible fluid, International Institute
for Advanced Study, IIAS Report No. 1996-003, ed. T. Miwa, pp. 11--30.
- 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
- H. Okamoto
and M Shoji, Boundary layer in unsteady two-dimensional Navier-Stokes
equations, ibid, pp. 171--180.
- 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
- 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.
- 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.
- (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.
- 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
- 岡本 久、R.
Finn 教授講演記録、数学、第33巻(1981), p84.
- 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.
- 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.
- 岡本 久, 定常表面張力波について, ながれ, vol. 13 (1994), pp. 184--195.
- 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).
- 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
- 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).
- 岡本 久、数値解析と応用数学関連の報告、数学、第51巻(1999), p210--212.
- 岡本 久,
Navier-Stokes 方程式の解の構造, ながれ, vol. 19 (2000), pp. 172--179.
- 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
- 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.
- 岡本 久, Proudmann-Johnson方程式の周辺の話題, 数理解析研究所講究録, 第1225巻,
(2001), pp. 176-179.
- 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, 第1231巻, (2001), pp. 69-82.
- (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。
- 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)
- 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巻(2003), 102--106 PS file , PDF file
- 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.
- 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. 88、2003年 8月号、32ページ. HTML
版
- (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.
- 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.
- 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, 第1368巻,
(2004), pp. 136-143.
- 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,253ぺーじ, 一般の書店でも購入できます)
- ニュートン法の話、「数学のたのしみ」2006年春号、70--91.
- 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.
- 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.
- ナヴィエ-ストークス方程式の導き方, 「数理科学」、2010年11月号、71--77.
- 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.
- 流体力学の厳密解、「数理科学」2012年11月号、
- 流体力学と数学、「数学通信」, 第18巻 第2号 (2013年), 6-12.
- 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。
- 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
- 関数概念の発展、長岡亮介氏との共著、近代科学社