Iguchi, Tatsuo

写真a

Affiliation

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

Position

Professor

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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

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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

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Academic Degrees 【 Display / hide 】

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

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Research Areas 【 Display / hide 】

  • Natural Science / Basic analysis (Basic Analysis)

  • Natural Science / Mathematical analysis (Global Analysis)

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Papers 【 Display / hide 】

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness

    Duchêne V., Iguchi T.

    Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire （Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire)  41 （ 2 ） 257 - 315 2024

    ISSN  02941449

    　View Summary

    We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well known, the full model for interfacial gravity waves has a variational structure whose Lagrangian is an extension of Luke’s Lagrangian for surface gravity waves, that is, water waves. The Kakinuma model is a system of Euler–Lagrange equations for approximate Lagrangians, which are obtained by approximating the velocity potentials in the Lagrangian for the full model. In this paper we first analyze the linear dispersion relation for the Kakinuma model and show that the dispersion curves highly fit that of the full model in the shallow water regime. We then analyze the linearized equations around constant states and derive a stability condition, which is satisfied for small initial data when the denser water is below the lighter water. We show that the initial value problem is in fact well posed locally in time in Sobolev spaces under the stability condition, the noncavitation assumption, and intrinsic compatibility conditions, in spite of the fact that the initial value problem for the full model does not have any stability domain so that its initial value problem is ill posed in Sobolev spaces. Moreover, it is shown that the Kakinuma model enjoys a Hamiltonian structure and has conservative quantities: mass, total energy, and in the case of a flat bottom, momentum.

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: Justification as a shallow water approximation

    Duchêne V., Iguchi T.

    Proceedings of the Royal Society of Edinburgh Section A: Mathematics （Proceedings of the Royal Society of Edinburgh Section A: Mathematics)   2024

    ISSN  03082105

    　View Summary

    We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler-Lagrange equations for an approximate Lagrangian, which is obtained by approximating the velocity potentials in the Lagrangian of the full model. Structures of the Kakinuma model and the well-posedness of its initial value problem were analysed in the companion paper [14]. In this present paper, we show that the Kakinuma model is a higher order shallow water approximation to the full model for interfacial gravity waves with an error of order in the sense of consistency, where and are shallowness parameters, which are the ratios of the mean depths of the upper and the lower layers to the typical horizontal wavelength, respectively, and is, roughly speaking, the size of the Kakinuma model and can be taken an arbitrarily large number. Moreover, under a hypothesis of the existence of the solution to the full model with a uniform bound, a rigorous justification of the Kakinuma model is proved by giving an error estimate between the solution to the Kakinuma model and that of the full model. An error estimate between the Hamiltonian of the Kakinuma model and that of the full model is also provided.

  • A priori estimates for solutions to equations of motion of an inextensible hanging string

    Iguchi T., Takayama M.

    Mathematische Annalen （Mathematische Annalen)   2024

    ISSN  00255831

    　View Summary

    We consider the initial boundary value problem to equations of motion of an inextensible hanging string of finite length under the action of the gravity. We also consider the problem in the case without any external forces. In this problem, the tension of the string is also an unknown quantity. It is determined as a unique solution to a two-point boundary value problem, which is derived from the inextensibility of the string together with the equation of motion, and degenerates linearly at the free end. We derive a priori estimates for solutions to the initial boundary value problem in weighted Sobolev spaces under a natural stability condition. The necessity for the weights results from the degeneracy of the tension. Uniqueness of solutions is also proved.

  • Hyperbolic free boundary problems and applications to wave-structure interactions

    T. Iguchi, D. Lannes

    Indiana University Mathematics Journal （Indiana University)  70 （ 1 ） 353 - 464 2021

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  00222518

    　View Summary

    Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly hyperbolic N × N quasilinear hyperbolic systems, we derive new sharp linear estimates with refined dependence on the source term and control on the traces of the solution at the boundary. These new estimates are used to obtain sharp results for quasilinear IBVP and transmission problems, and we also use them to propose a general approach to 2 × 2 quasilinear IBVP and transmission problems with a moving or possibly free boundary. In the latter case, two kinds of evolution equations for the boundary are considered. The first one is of “kinematic type” in the sense that the velocity of the interface has the same regularity as the trace of the solution. Several applications that fall into this category are considered: the interaction of waves with a lateral piston, and a new version of the well-known stability of shocks (classical and undercompressive) that improves the results of the general theory by taking advantage of the specificities of the one-dimensional case. We also consider “fully nonlinear” evolution equations characterized by the fact that the velocity of the interface is one derivative more singular than the trace of the solution. This configuration is the most challenging; it is motivated by a free boundary problem arising in wave-structure interaction: namely, the evolution of the contact line between a floating object and the water. This problem is solved as an application of the general theory developed here.

  • Isobe-Kakinuma model for water waves

    T. Iguchi

    Mathematics for Industry （Springer)  34   181 - 191 2020.08

    Research paper (international conference proceedings), Single Work, Accepted

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

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Presentations 【 Display / hide 】

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves

    井口達雄

    RIMS共同研究（公開型）「流体と気体の数学解析」 (京都大学数理解析研究所 (online)) , 

    2021.07
    , 

    Oral presentation (general)

  • A Hamiltonian structure of the Isobe-Kakinuma model for water waves

    Tatsuo Iguchi

    Workshop on Free Surface Hydrodynamics (The Fields Institute for Research in Mathmatical Sciences (online)) , 

    2020.10
    , 

    Oral presentation (invited, special)

  • 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 lecture, seminar, tutorial, course, or other speech

  • 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 lecture, seminar, tutorial, course, or other speech

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

  • 水の波の数学解析の新展開

    2022.04
    -
    2027.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(B), Principal investigator

  • 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, Grant-in-Aid for Challenging Research (Exploratory) , Principal investigator

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Awards 【 Display / hide 】

  • IOP Outstanding Reviewer Awards 2018 (Nonlinearity)

    2019.03

    Type of Award： Honored in official journal of a scientific society, scientific 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： Award from Japanese society, conference, symposium, etc.

  • 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： Award from publisher, newspaper, foundation, etc.

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Courses Taught 【 Display / hide 】

  • TOPICS IN FUNCTIONAL EQUATIONS A

    2024

  • PRINCIPLES OF FUNCTIONAL EQUATIONS

    2024

  • MATHEMATICS 2B

    2024

  • MATHEMATICS 2A

    2024

  • MATHEMATICS 1B

    2024

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    1994
    -
    Present
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