Updated on 2025/04/09

Information

 

写真a

 
TAKEUCHI TAIKI
 
Organization
Institute of Mathematics for Industry Division of Advanced Mathematics Technology Assistant Professor
Title
Assistant Professor
External link

Research Areas

  • Natural Science / Mathematical analysis

Degree

  • 博士(理学) （ 2023.3 Waseda University ）

Research History

  • Kyushu University Institute of Mathematics for Industry Assistant Professor 

    2024.10 - Present

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    Country：Japan

  • Kanagawa University Faculty of Engineering Part-time Teacher 

    2024.4 - Present

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    Country：Japan

  • Kyoto University Graduate School of Science Research Fellowship for Young Scientists (PD) 

    2024.4 - 2024.9

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    Country：Japan

  • Waseda University Faculty of Science and Engineering Research Fellowship for Young Scientists (PD) 

    2023.4 - 2024.3

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    Country：Japan

  • Waseda University Graduate School of Fundamental Science and Engineering Research Fellowship for Young Scientists (DC2) 

    2022.4 - 2023.3

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    Country：Japan

Education

  • Waseda University   Graduate School of Fundamental Science and Engineering   Doctoral Program in Department of Pure and Applied Mathematics

    2021.4 - 2023.3

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    Country：Japan

  • Waseda University   Graduate School of Fundamental Science and Engineering   Master's Program in Department of Pure and Applied Mathematics

    2020.4 - 2021.3

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    Country：Japan

    Notes：Master's Program (Early comletion)

  • Waseda University   School of Fundamental Science and Engineering   Department of Mathematics

    2017.4 - 2020.3

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    Country：Japan

Research Interests・Research Keywords

  • Research theme： Theory of Partial Differential Equations

    Keyword： Partial Differential Equations

    Research period： 2021 - Present

Awards

Papers

  • Mild solutions of the MHD system with external forces in scaling invariant Besov spaces Reviewed International journal

    Taichi Eguchi; Taiki Takeuchi

    Zeitschrift für angewandte Mathematik und Physik   76 ( 2 )   Paper No. 62, 26 pp   2025.4   （ ISSN:0044-2275 eISSN:1420-9039 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    The incompressible MHD system with external forces in the whole space is considered. We show the unique existence theorem of local mild solutions to the MHD system for given initial data and external forces in scaling invariant Besov spaces framework. We also obtain global mild solutions for small initial data and external forces. In addition, by assuming suitable additional conditions for initial data and external forces, we reveal that the global mild solutions have some time-decay properties with respect to the scaling invariant norms.

    DOI： doi.org/10.1007/s00033-025-02435-8

    Other Link： https://link.springer.com/article/10.1007/s00033-025-02435-8/fulltext.html

    Repository Public URL： https://hdl.handle.net/2324/7337399

  • Refined Interpolation Inequality in Besov Spaces With Applications to the Gagliardo--Nirenberg Inequality Reviewed International journal

    Tohru Ozawa; Taiki Takeuchi

    Asymptotic Analysis   141 ( 2 )   119 - 131   2025.2

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    We consider the interpolation inequality with respect to the regularity index in homogeneous Besov spaces. By choosing a general summability index and estimating carefully, we reveal a precise representation of the constant appearing in the interpolation inequality. As an application of the refined interpolation inequality, we show a generalization of the Gagliardo-Nirenberg inequality in homogeneous Besov spaces given by Wadade (2006).

    DOI： doi.org/10.1177/09217134241308362

  • Well‐posedness and inviscid limits for the Keller–Segel–Navier–Stokes system of the parabolic–elliptic type Reviewed International journal

    Taiki Takeuchi

    Mathematische Nachrichten   298 ( 1 )   53 - 86   2025.1   （ ISSN:0025-584X eISSN:1522-2616 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Wiley  

    We show the local well-posedness of the Keller-Segel system of parabolic-elliptic type coupled with the Navier-Stokes system for arbitrary initial data with Sobolev regularities, where the solution is uniformly bounded with respect to the viscosity. We also show the continuous dependence of the solutions with respect to the initial data. As a result of the uniform boundedness of the solutions, we obtain inviscid limits of the above system. The proof is mainly based on a priori estimates in the Sobolev spaces.

    DOI： 10.1002/mana.202300304

  • Asymptotic behavior of global mild solutions to the Keller-Segel-Navier-Stokes system in Lorentz spaces Reviewed International journal

    Taiki Takeuchi

    to appear in Advances in Nonlinear Analysis   2025

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    Language：English   Publishing type：Research paper (scientific journal)  

    The Keller-Segel-Navier-Stokes system in the whole space is considered. We show the existence and uniqueness of local mild solutions for arbitrary initial data and gravitational potential in scaling invariant Lorentz spaces. Although such a result has already been shown by Kozono, Miura, and Sugiyama (2016), we reveal the precise regularities of mild solutions by showing the smoothing estimates of the heat semigroup on Lorentz spaces. The method is based on the real interpolation. In addition, we prove that the mild solutions exist globally in time provided that the initial data are sufficiently small. Compared with the usual result, a part of the smallness conditions is reduced. We also obtain the asymptotic behavior of the global mild solutions. In the proof of the asymptotic behavior, to overcome a lack of density for the space to which one of the initial data belongs, we show the decay of the global solutions without any approximation for such an initial datum.

  • A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach Reviewed International journal

    Tohru Ozawa; Taiki Takeuchi

    Proceedings of the American Mathematical Society, Series B   11   371 - 377   2024.7   （ eISSN:2330-1511 ）

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    We give a new proof of the Gagliardo-Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo-Nirenberg inequality, we simplify the previous proof by relying only on the fundamental estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.

    DOI： 10.1090/bproc/211

    Repository Public URL： https://hdl.handle.net/2324/7325988

  • Breakdown of C^∞-smoothing effects of solutions to the semilinear equation in the whole space Reviewed International journal

    Taiki Takeuchi

    Communications on Pure and Applied Analysis   23 ( 6 )   830 - 872   2024.6

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    Language：English   Publishing type：Research paper (scientific journal)  

    The semilinear heat equation in the whole space is considered, where the nonlinear terms are given as the forms of non-integer power types. In particular, we focus on global solutions for small initial data in the scaling invariant Lebesgue spaces. We reveal that the global solutions have a certain regularity. Moreover, by taking special initial data, we show that the global solutions are not smooth in space. From these results, we reveal a threshold of the regularity in space. The proof relies on the estimates of higher order derivatives of the nonlinear terms.

    DOI： 10.3934/cpaa.2024037

    Repository Public URL： https://hdl.handle.net/2324/7325987

  • Remarks on the smoothing effect of the heat semigroup on Ḃ_{p,∞}^s(R^n) Reviewed International journal

    Taiki Takeuchi

    Partial Differential Equations in Applied Mathematics   10   100718   2024.6   （ ISSN:2666-8181 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We consider the heat semigroup defined on homogeneous Besov spaces whose interpolation index is infinity. We show the strong time-continuity of the heat semigroup for fixed positive time variables. In addition, we reveal a sufficient condition of functions in the domain for the strong convergence to themselves as time tends to zero. We also give counterexamples of functions that do not provide such a strong convergence.

    DOI： 10.1016/j.padiff.2024.100718

    Repository Public URL： https://hdl.handle.net/2324/7325986

  • Refined Decay Estimate and Analyticity of Solutions to the Linear Heat Equation in Homogeneous Besov Spaces Reviewed International journal

    Tohru Ozawa; Taiki Takeuchi

    Journal of Fourier Analysis and Applications   29 ( 5 )   Paper No. 61, 27 pp   2023.10   （ ISSN:1069-5869 eISSN:1531-5851 ）

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    The heat semigroup defined on homogeneous Besov spaces is considered. We show the decay estimate of solutions to the linear heat equation with an explicit bound depending only on the regularity index and space dimension. It may be regarded as a refined result compared with that of the second author (2021). As a result of the refined decay estimate, we also improve a lower bound estimate of the radius of convergence of the Taylor expansion of such a solution in space and time. To refine the previous results, we show explicit pointwise estimates of higher order derivatives of the power function. In addition, we also refine a certain estimate of the derivatives of the heat kernel.

    DOI： 10.1007/s00041-023-10042-2

    Other Link： https://link.springer.com/article/10.1007/s00041-023-10042-2/fulltext.html

    Repository Public URL： https://hdl.handle.net/2324/7329951

  • Various regularity estimates for the Keller-Segel-Navier-Stokes system in Besov spaces Reviewed International journal

    Taiki Takeuchi

    Journal of Differential Equations   343   606 - 658   2023.1   （ ISSN:0022-0396 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We show the local well-posedness for the Keller-Segel-Navier-Stokes system with initial data in the scaling invariant Besov spaces, where the solution exists globally in time if the initial data is sufficiently small. We also reveal that the solution belongs to the Lorentz spaces in time direction, while the solution is smooth in space and time. Moreover, we obtain the maximal regularity estimates of solutions under certain conditions. We further show that the solution has additional regularities if the initial data has higher regularities. This result implies that global solutions decay as time tends to infinity in the same norm of the space of the initial data. Our results on the Lorentz regularity estimates are based on the strategy by Kozono and Shimizu (2019).

    DOI： 10.1016/j.jde.2022.10.035

    Repository Public URL： https://hdl.handle.net/2324/7325984

  • Maximal Lorentz regularity for the Keller–Segel system of parabolic–elliptic type Reviewed International journal

    Taiki Takeuchi

    Journal of Evolution Equations   21 ( 4 )   4619 - 4640   2021.12   （ ISSN:1424-3199 eISSN:1424-3202 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    We construct local strong solutions of the Keller-Segel system of parabolic-elliptic type for arbitrary initial data in the scaling invariant homogeneous Besov spaces. We also show that the solution exists globally in time for small initial data. The solutions belong to the Lorentz space in time direction since our method relies on the maximal Lorentz regularity theorem of the linear heat equation.

    DOI： 10.1007/s00028-021-00728-9

    Web of Science

    Repository Public URL： https://hdl.handle.net/2324/7325982

  • Space–time analytic smoothing effect of the heat semigroup defined on homogeneous Besov spaces Reviewed International journal

    Taiki Takeuchi

    Partial Differential Equations in Applied Mathematics   4   100174   2021.12   （ ISSN:2666-8181 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We refine the decay estimate of the heat semigroup defined on homogeneous Besov spaces, which is obtained by Kozono, Ogawa, and Taniuchi (2003). In particular, we give an explicit representation of a constant appearing in the decay estimate for the heat semigroup, which provides a space-time analytic smoothing effect. As a by-product, we obtain a radius of convergence of the Taylor expansion exactly. Furthermore, it is also shown that the heat semigroup is a bounded analytic continuous semigroup under certain conditions, where it can be extended as an analytic function of time variable on the sector with an explicitly given angle.

    DOI： 10.1016/j.padiff.2021.100174

    Repository Public URL： https://hdl.handle.net/2324/7325983

  • The Keller-Segel system of parabolic-parabolic type in homogeneous Besov spaces framework Reviewed International journal

    Taiki Takeuchi

    Journal of Differential Equations   298   609 - 640   2021.10   （ ISSN:0022-0396 ）

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    We show the existence and uniqueness of local strong solutions of the Keller-Segel system of parabolic-parabolic type for arbitrary initial data in the scaling invariant homogeneous Besov spaces. We also construct global strong solutions for small initial data, where the solutions belong to the Lorentz space in time direction. The proof is based on the maximal Lorentz regularity theorem of the linear heat equation.

    DOI： 10.1016/j.jde.2021.07.018

    Web of Science

    Repository Public URL： https://hdl.handle.net/2324/7325981

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Presentations

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Professional Memberships

Academic Activities

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Research Projects

  • Solvability and regularity of solutions for the chemotaxis system by the method of functional analysis

    Grant number：24K16954  2024.4 - 2029.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Early-Career Scientists

    Taiki Takeuchi

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    Authorship：Principal investigator  Grant type：Scientific research funding

    本研究では，細胞が凝集を行う現象として知られる走化性現象を記述する数理モデルの解析を行う．なお，走化性現象は傷の治癒現象やがん細胞の転移現象などに応用される生物医学的に重要な性質である．本研究では，数理モデルの初期値問題のうち，初期値の特異性が極めて強い場合を考察する．具体的には，不連続な可測関数や，測度などを含む超関数の枠組みを扱い，対応する初期値問題の可解性について調査する．また対応する解の滑らかさを考察することで，非常に強い特異性を持つ初期条件に対しても，走化性現象の数理モデルが十分な平滑化作用を与えることを示す．

  • Maximal regularity theory of the Fujita-type equation based on the harmonic analysis

    Grant number：24KJ0122  2024.4 - 2027.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for JSPS Fellows

    Taiki Takeuchi

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    Authorship：Principal investigator  Grant type：Scientific research funding

  • Analysis of the double chemotaxis model with the effect of fluid

    Grant number：22KJ2930  2023.3 - 2024.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for JSPS Fellows

    Taiki Takeuchi

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    Authorship：Principal investigator  Grant type：Scientific research funding

  • Analysis of the double chemotaxis model with the effect of fluid

    Grant number：22J12100  2022.4 - 2023.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for JSPS Fellows

    Taiki Takeuchi

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    Authorship：Principal investigator  Grant type：Scientific research funding

  • Analysis of the double chemotaxis model with the effect of fluid

    Grant number：MJSP2128  2021.10 - 2022.3

    Japan Science and Technology Agency  JST Support for Pioneering Research Initiated by the Next Generation (SPRING) 

    Taiki Takeuchi

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    Authorship：Principal investigator  Grant type：Competitive funding other than Grants-in-Aid for Scientific Research

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2024  神奈川大学  Classification:Part-time lecturer  Domestic/International Classification:Japan 

Travel Abroad

  • 2023.1 - 2023.3

    Staying countory name 1：Germany   Staying institution name 1：パーダーボルン大学

    Staying institution name 2：ハノーファー大学