井口 達雄 (イグチ タツオ)

Iguchi, Tatsuo

写真a

所属(所属キャンパス)

理工学部 数理科学科 (矢上)

職名

教授

HP

外部リンク

経歴 【 表示 / 非表示

  • 1997年01月
    -
    2002年03月

    九州大学大学院数理学研究科文部教官助手

  • 2002年04月
    -
    2006年03月

    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年04月
    -
    2011年03月

    慶應義塾大学理工学部助教授

  • 2011年04月
    -
    継続中

    慶應義塾大学理工学部教授

学歴 【 表示 / 非表示

  • 1993年03月

    早稲田大学, 理工学部, 数学科

    大学, 卒業

  • 1995年04月

    早稲田大学, 理工学研究科, 数理科学専攻

    大学院, 修了, 修士

  • 1996年12月

    早稲田大学, 理工学研究科, 数理科学専攻

    大学院, 退学, 博士

学位 【 表示 / 非表示

  • On the Well-Posedness of Initial Value Problems for Ideal Fluid with Free Boundary, 早稲田大学, 論文, 1998年03月

 

研究分野 【 表示 / 非表示

  • 自然科学一般 / 基礎解析学 (基礎解析学)

  • 自然科学一般 / 数理解析学 (大域解析学)

 

論文 【 表示 / 非表示

  • Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string

    井口 達雄,高山 正宏

    Osaka Journal of Mathematics 2025年

    研究論文(学術雑誌), 査読有り,  ISSN  0030-6126

     概要を見る

    Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems with a localized term and show its well-posedness in weighted Sobolev spaces. We then consider the linearized system for the motion of an inextensible hanging string. Well-posedness of its initial boundary value problem is demonstrated as an application of the result obtained in the first part.

  • The 2D nonlinear shallow water equations with a partially immersed obstacle

    Iguchi, T., Lannes D.

    Journal of the European Mathematical Society (The Publishing House of the European Mathematical Society)  2025年

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  1435-9855

     概要を見る

    This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension d=2 and in the presence of a fixed partially immersed object. We first show that this wave-interaction problem reduces to an initial boundary value problem for the nonlinear shallow water equations in an exterior domain, with boundary conditions that are fully nonlinear and nonlocal in space and time. This hyperbolic initial boundary value problem is characteristic, does not satisfy the constant rank assumption on the boundary matrix, and the boundary conditions do not satisfy any standard form of dissipativity. Our main result is the well-posedness of this system for irrotational data and at the quasilinear regularity threshold. In order to prove this, we introduce a new notion of weak dissipativity, that holds only after integration in time and space. This weak dissipativity allows higher order energy estimates without derivative loss; the analysis is carried out for a class of linear non-characteristic hyperbolic systems, as well as for a class of characteristic systems that satisfy an algebraic structural property that allows us to define a generalized vorticity. We then show, using a change of unknowns, that it is possible to transform the linearized wave-interaction problem into a non-characteristic system, which satisfies this structural property and for which the boundary conditions are weakly dissipative. We can therefore use our general analysis to derive linear, and then nonlinear, a priori energy estimates. Existence for the linearized problem is obtained by a regularization procedure that makes the problem non-characteristic and strictly dissipative, and by the approximation of the data by more regular data satisfying higher order compatibility conditions for the regularized problem. Due to the fully nonlinear nature of the boundary conditions, it is also necessary to implement a quasilinearization procedure. Finally, we have to lower the standard requirements on the regularity of the coefficients of the operator in the linear estimates to be able to reach the quasilinear regularity threshold in the nonlinear well-posedness result.

  • 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 (Cambridge University Press)  2024年03月

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  0308-2105

     概要を見る

    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 (Springer)  390   1919 - 1971 2024年01月

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  0025-5831

     概要を見る

    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.

  • 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 (The Publishing House of the European Mathematical Society)  41 ( 2 ) 257 - 315 2023年03月

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  0294-1449

     概要を見る

    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.

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総説・解説等 【 表示 / 非表示

  • The water wave equations

    Iguchi T.

    Sugaku Expositions (American Mathematical Society)  35 ( 1 ) 53 - 81 2022年04月

    記事・総説・解説・論説等(学術雑誌), 単著,  ISSN  0898-9583

  • 水の波の方程式

    井口 達雄

    雑誌『数学』 (日本数学会)  70 ( 1 ) 1 - 25 2018年01月

    記事・総説・解説・論説等(学術雑誌), 単著,  ISSN  0039-470X

研究発表 【 表示 / 非表示

  • 吊り下げられた紐の運動に対する初期境界値問題の適切性

    高山 正宏,井口 達雄

    日本数学会年会 (早稲田大学) , 

    2025年03月

    口頭発表(一般), 日本数学会

  • 局所化項をもつ退化双曲系に対する初期境界値問題の適切性

    高山 正宏,井口 達雄

    日本数学会秋季総合分科会 (大阪大学) , 

    2024年09月

    口頭発表(一般), 日本数学会

  • 吊り下げられた紐の運動に対する線形化問題の適切性

    高山 正宏,井口 達雄

    日本数学会秋季総合分科会 (大阪大学) , 

    2024年09月

    口頭発表(一般), 日本数学会

  • 吊り下げられた紐の運動に対する解のアプリオリ評価

    高山 正宏,井口 達雄

    日本数学会年会 (大阪公立大学) , 

    2024年03月

    口頭発表(一般), 日本数学会

  • 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年07月

    口頭発表(一般)

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競争的研究費の研究課題 【 表示 / 非表示

  • 水の波の数学解析の新展開

    2022年04月
    -
    2027年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 井口 達雄, 基盤研究(B), 補助金,  研究代表者

  • 水の波の新しいモデルの創出とその数学解析

    2017年06月
    -
    2020年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 井口 達雄, 挑戦的研究(萌芽), 補助金,  研究代表者

受賞 【 表示 / 非表示

  • IOP Outstanding Reviewer Awards 2021 (Journal of Physics A: Mathematical and Theoretical)

    2022年04月

    受賞区分: 学会誌・学術雑誌による顕彰

  • IOP Outstanding Reviewer Awards 2018 (Nonlinearity)

    2019年03月

    受賞区分: 学会誌・学術雑誌による顕彰

  • 日本数学会 函数方程式論分科会 福原賞

    井口 達雄, 2010年12月, 水面波方程式の数学解析の研究

    受賞区分: 国内学会・会議・シンポジウム等の賞

  • 手島工業教育資金団藤野研究賞

    井口 達雄, 2003年03月, 水面波の方程式の解析的研究

    受賞区分: 出版社・新聞社・財団等の賞

 

担当授業科目 【 表示 / 非表示

  • 関数方程式概論

    2025年度

  • 数学2B

    2025年度

  • 数学2A

    2025年度

  • 数学解析第2

    2025年度

  • 基礎理工学課題研究

    2025年度

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所属学協会 【 表示 / 非表示

  • 日本数学会, 

    1994年
    -
    継続中