Iguchi, Tatsuo

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Professor

Related Websites

External Links

Career 【 Display / hide

  • 1997.01
    -
    2002.03

    九州大学大学院数理学研究科文部教官助手

  • 2002.04
    -
    2006.03

    東京工業大学大学院理工学研究科文部科学教官助教授

  • 2006.04
    -
    2011.03

    慶應義塾大学理工学部助教授

  • 2011.04
    -
    Present

    慶應義塾大学理工学部教授

Academic Background 【 Display / hide

  • 1993.03

    Waseda University, Faculty of Science and Engineering, Department of Mathematics

    University, Graduated

  • 1995.04

    Waseda University, Graduate School, Division of Science and Engineering, 数理科学専攻

    Graduate School, Completed, Master's course

  • 1996.12

    Waseda University, Graduate School, Division of Science and Engineering, 数理科学専攻

    Graduate School, Withdrawal before completion, Doctoral course

Academic Degrees 【 Display / hide

  • On the Well-Posedness of Initial Value Problems for Ideal Fluid with Free Boundary, Waseda University, Dissertation, 1998.03

 

Research Areas 【 Display / hide

  • Basic analysis (Basic Analysis)

  • Mathematical analysis (Global Analysis)

 

Papers 【 Display / hide

  • Motion of a vortex filament in an external flow

    Masashi Aiki, Tatsuo Iguchi

    Nonlinearity (IOP Publishing)  32 ( 7 ) 4213 - 4225 2019.05

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  09517715

     View Summary

    We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take into account the effect of external flow. We prove the unique solvability, locally in time, of an initial value problem posed on the one dimensional torus. The problem describes the motion of a closed vortex filament.

  • A Mathematical Justification of the Isobe–Kakinuma Model for Water Waves with and without Bottom Topography

    Iguchi T.

    Journal of Mathematical Fluid Mechanics (Journal of Mathematical Fluid Mechanics)  20 ( 4 ) 1985 - 2018 2018.12

    ISSN  14226928

     View Summary

    © 2018, Springer Nature Switzerland AG. We consider the Isobe–Kakinuma model for water waves in both cases of the flat and the variable bottoms. The Isobe–Kakinuma model is a system of Euler–Lagrange equations for an approximate Lagrangian which is derived from Luke’s Lagrangian for water waves by approximating the velocity potential in the Lagrangian appropriately. The Isobe–Kakinuma model consists of (N+ 1) second order and a first order partial differential equations, where N is a nonnegative integer. We justify rigorously the Isobe–Kakinuma model as a higher order shallow water approximation in the strongly nonlinear regime by giving an error estimate between the solutions of the Isobe–Kakinuma model and of the full water wave problem in terms of the small nondimensional parameter δ, which is the ratio of the mean depth to the typical wavelength. It turns out that the error is of order O(δ4N+2) in the case of the flat bottom and of order O(δ4[N/2]+2) in the case of variable bottoms.

  • Isobe–Kakinuma model for water waves as a higher order shallow water approximation

    Iguchi T.

    Journal of Differential Equations (Journal of Differential Equations)  265 ( 3 ) 935 - 962 2018.08

    ISSN  00220396

     View Summary

    © 2018 Elsevier Inc. We justify rigorously an Isobe–Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order O(δ2), where δ is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength. The Green–Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order O(δ4). In this paper we show that the Isobe–Kakinuma model is a much higher order approximation to the water wave equations with an error of order O(δ6).

  • Solvability of the Initial Value Problem to the Isobe–Kakinuma Model for Water Waves

    Nemoto R., Iguchi T.

    Journal of Mathematical Fluid Mechanics (Journal of Mathematical Fluid Mechanics)  20 ( 2 ) 631 - 653 2018.06

    ISSN  14226928

     View Summary

    © 2017, Springer International Publishing AG. We consider the initial value problem to the Isobe–Kakinuma model for water waves and the structure of the model. The Isobe–Kakinuma model is the Euler–Lagrange equations for an approximate Lagrangian which is derived from Luke’s Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe–Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t= 0 is characteristic for the Isobe–Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh–Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

  • A mathematical justification of a thin film approximation for the flow down an inclined plane

    UENO Hiroki, IGUCHI Tatsuo

    Journal of Mathematical Analysis and Applications (Elsevier)  444 ( 1 ) 804 - 824 2016.12

    Research paper (scientific journal), Joint Work, Accepted

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Papers, etc., Registered in KOARA 【 Display / hide

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Presentations 【 Display / hide

  • 磯部‐柿沼モデルの孤立波解とその極限波

    井口達雄

    海洋・海岸における波動の解析モデルの発展 (九州大学応用力学研究所) , 2019.12, Oral Presentation(general)

  • Initial value problem to a shallow water model with a floating solid body

    井口達雄

    神戸大学解析セミナー (神戸大学理学部) , 2019.11, Public discourse, seminar, tutorial, course, lecture and others

  • Initial value problem to a shallow water model with a floating solid body

    井口達雄

    九州関数方程式セミナー (福岡大学セミナーハウス) , 2019.11, Public discourse, seminar, tutorial, course, lecture and others

  • Initial value problem to a shallow water model with a floating solid body

    井口達雄

    非線形波動現象の数理とその応用 (京都大学数理解析研究所) , 2019.10, Oral Presentation(general)

  • Initial value problem to a shallow water model with floating structures

    井口達雄

    偏微分方程式待兼山セミナー (大阪大学数学教室) , 2019.09, Public discourse, seminar, tutorial, course, lecture and others

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • 水の波の新しいモデルの創出とその数学解析

    2017.06
    -
    2020.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 井口 達雄, Grant-in-Aid for Challenging Research (Exploratory) , Principal Investigator

Awards 【 Display / hide

  • IOP Outstanding Reviewer Awards 2018 (Nonlinearity)

    2019.03

    Type of Award: Celebration by Official journal of a scientific society or Academic Journal

  • 日本数学会 函数方程式論分科会 福原賞

    IGUCHI Tatsuo, 2010.12, 水面波方程式の数学解析の研究

    Type of Award: Awards of National Conference, Council and Symposium

  • 手島工業教育資金団藤野研究賞

    IGUCHI Tatsuo, 2003.03, 水面波の方程式の解析的研究

    Type of Award: Awards of Publisher, Newspaper Company and Foundation

 

Courses Taught 【 Display / hide

  • TOPICS IN FUNCTIONAL EQUATIONS A

    2020

  • PRINCIPLES OF FUNCTIONAL EQUATIONS

    2020

  • MATHEMATICS 3B

    2020

  • MATHEMATICS 3A

    2020

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2020

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Memberships in Academic Societies 【 Display / hide

  • 日本数学会, 

    1994
    -
    Present