Updated on 2022/03/24

FUJIWARA Kazumasa

Organization
Graduate School of Mathematics Social Mathematics Assistant Professor
School of Science Department of Mathematics

### Degree 1

1. Doctor of Science （ 2017.3   Waseda University ）

### Research Interests 5

1. Blowup

2. Damped wave equation

3. Fractional Calculus

4. PDE

5. Schrodinger equation

### Research Areas 1

1. Natural Science / Mathematical analysis  / PDE Analysis

### Research History 7

1. Nagoya University   Graduate School of Mathematics   Assistant Professor

2020.10

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Country：Japan

2. Japan Society for Promotion of Science   JSPS Superlative Postdoctoral Fellow: SPD

2019.4 - 2020.9

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Country：Japan

3. Scuola Normale Superiore di Pisa   Centro di Ricerca Matematica Ennio De Giorgi   Junior Visiting Position

2017.10 - 2019.3

4. Chuo University   Part-time Lecturer

2017.4 - 2017.9

5. Japan Society for Promotion of Science   JSPS Research Fellow: PD

2017.4 - 2017.9

6. Japan Society for Promotion of Science   JSPS Research Fellow: DC2

2016.4 - 2017.3

7. Japan Society for Promotion of Science   JSPS Research Fellow: DC1

2014.4 - 2016.3

### Education 1

1. Waseda University   School of Advaned Science and Engineering   Doctor Corse, Department of Pure and Applied Physics

2014.4 - 2017.3

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Country： Japan

### Professional Memberships 2

1. The International Society for Analysis, its Applications and Computation (ISAAC) : Life Member

2. THE MATHEMATICAL SOCIETY OF JAPAN

### Papers 14

1. Higher Order Fractional Leibniz Rule Reviewed International coauthorship International journal

Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

Journal of Fourier Analysis and Applications   Vol. 24 ( 3 ) page： 650 - 665   2018.6

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

The fractional Leibniz rule is generalized by the Coifman–Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.

2. On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity Reviewed International coauthorship International journal

Journal of Mathematical Physics   Vol. 62 ( 9 ) page： 091504 - 091504   2021.9

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

We study the 1D nonlinear Schrödinger equation with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global dispersive solutions, which are constant with respect to space. The non-existence of global solutions has also been studied only by focusing on the behavior of the Fourier 0 mode of solutions. However, the earlier works are not sufficient to obtain the precise criteria for the global existence for the Cauchy problem. In this paper, the exact criteria for the global existence of L2 solutions are shown by studying the interaction between the Fourier 0 mode and oscillation of solutions. Namely, L2 solutions are shown a priori not to exist globally if they are different from the trivial ones.

3. A test function method for evolution equations with fractional powers of the Laplace operator Reviewed International coauthorship International journal

M. D’Abbicco, K. Fujiwara

Nonlinear Analysis   Vol. 202   page： 112114 - 112114   2021.1

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

4. Self-similar solutions to the derivative nonlinear Schrödinger equation Reviewed International coauthorship

Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

Journal of Differential Equations   Vol. 268 ( 12 ) page： 7940 - 7961   2020.6

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

A class of self-similar solutions to the derivative nonlinear Schrödinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

5. Lifespan of Solutions for a Weakly Coupled System of Semilinear Heat Equations

Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi

TOKYO JOURNAL OF MATHEMATICS   Vol. 43 ( 1 ) page： 163 - 180   2020.6

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：TOKYO JOURNAL MATHEMATICS EDITORIAL OFFICE ACAD CENTER

We introduce a direct method to analyze the blow-up of solutions to systems of ordinary differential inequalities, and apply it to study the blow-up of solutions to a weakly coupled system of semilinear heat equations. In particular, we give upper and lower estimates of the lifespan of the solution in the subcritical case.

6. On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases Reviewed International coauthorship International journal

Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

Journal de Mathématiques Pures et Appliquées   Vol. 136   page： 239 - 256   2020.4

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

In this paper, the global well-posedness of semirelativistic equations with a power type nonlinearity on Euclidean spaces is studied. In two dimensional $H^s$ scaling subcritical case with $1 \leq s \leq 2$, the local well-posedness follows from a Strichartz estimate. In higher dimensional $H^1$ scaling subcritical case, the local well-posedness for radial solutions follows from a weighted Strichartz estimate. Moreover, in three dimensional $H^1$ scaling critical case, the local well-posedness for radial solutions follows from a uniform bound of solutions which may be derived by the corresponding one dimensional problem. Local solutions may be extended by a priori estimates.

7. Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential Reviewed International coauthorship International journal

Luigi Forcella, Kazumasa FUJIWARA, Vladimir Georgiev, Tohru Ozawa

Discrete Contin. Dyn. Syst.   Vol. 39 ( 5 ) page： 2661 - 2678   2019

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

We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.

8. Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi

Funkcialaj Ekvacioj   Vol. 62 ( 2 ) page： 157 - 189   2019

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Division of Functional Equations, The Mathematical Society of Japan (JST)

We study estimates of lifespan and blow-up rates of solutions for the Cauchy problem of the wave equation with a time-dependent damping and a power-type nonlinearity. When the damping acts on the solutions effectively, and the nonlinearity belongs to the subcritical case, we show the sharp lifespan estimates and the blow-up rates of solutions. The upper estimates are proved by an ODE argument, and the lower estimates are given by a method of scaling variables.

9. Kazumasa Fujiwara

Mathematical Methods in the Applied Sciences     2018.9

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Publisher：Wiley

DOI： 10.1002/mma.4944

10. Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

Dynamics of Partial Differential Equations   Vol. 15 ( 3 ) page： 175 - 182   2018

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Press of Boston, Inc.

The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case, the optimal lifespan estimate for size of initial data is obtained.

11. Evol. Equ. Control Theory     2018

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12. Lifespan of strong solutions to the periodic nonlinear Schrodinger equation without gauge invariance Reviewed International journal

Kazumasa Fujiwara, Tohru Ozawa

JOURNAL OF EVOLUTION EQUATIONS   Vol. 17 ( 3 ) page： 1023 - 1030   2017.9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER BASEL AG

A lifespan estimate and sharp condition of the initial data for finite time blowup for the periodic nonlinear Schrodinger equation are presented from a viewpoint of the total signed densities of initial data.

13. BLOW-UP OF SOLUTIONS FOR WEAKLY COUPLED SYSTEMS OF COMPLEX GINZBURG-LANDAU EQUATIONS Reviewed International journal

Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS     page： Paper No. 196, 18   2017.8

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：TEXAS STATE UNIV

Blow-up phenomena of weakly coupled systems of several evolution equations, especially complex Ginzburg-Landau equations is shown by a straightforward ODE approach, not by the so-called test-function method used in [38] which gives the natural blow-up rate. The difficulty of the proof is that, unlike the single case, terms which come from the Laplacian cannot be absorbed into the weakly coupled nonlinearities. A similar ODE approach is applied to heat systems by Mochizuki [32] to obtain the lower estimate of lifespan.

14. Fujiwara Kazumasa, Miyazaki Hayato

RIMS K\^oky\^uroku Bessatsu, B63     page： 13   2017

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Publisher：Res. Inst. Math. Sci. (RIMS), Kyoto

### Presentations 24

1. Necessary and sufficient condition for global existence of L2 solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity Invited

Kazumasa Fujiwara

The 46th Sapporo Symposium on Partial Differential Equations  2021.8.12

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Event date： 2021.8

Language：Japanese   Presentation type：Oral presentation (invited, special)

2. 周期境界条件に於ける絶対値冪乗型の非線型項を有するシュレーディンガー方程式に対する 時間大域可解性の為の自乗可積分な初期状態の必要充分条件 Invited

Kazumasa Fujiwara

2021.4.12

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Event date： 2021.4

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech

3. Necessary and sufficient condition for global existence of $L^2$ solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity Invited

Kazumasa Fujiwara

2021.1.8

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Event date： 2021.1

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech

4. Necessary and sufficient condition for global existence of $L^2$ solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity Invited

Kazumasa Fujiwara

2020.12.11

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Event date： 2020.12

Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech

5. Necessary and sufficient condition of L^2 global existence for a periodic nonlinear Schrödinger equation Invited

Kazumasa Fujiwara

Webinar Critical exponent versus blow-up in evolution models  2020.12.8

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Event date： 2020.12

Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech

6. Non existence of time-local solutions to semilinear semirelativistic equation in some subcritical case Invited

Kazumasa Fujiwara

Dispersive and subelliptic PDEs  2020.2.12

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Event date： 2020.2

Language：English   Presentation type：Oral presentation (general)

7. An estimate for commutator of fractional Laplacian with rough metric International conference

Kazumasa FUJIWARA

International Workshop on “Fundamental Problems in Mathematical and Theoretical Physics”  2019.7.25  Mathematics and Physics Unit“ Multiscale Analysis, Modelling and Simulation ”

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Language：English   Presentation type：Oral presentation (general)

Venue：waseda university

We show an estimate for commutator of weight functions and fractional Laplacian with
rough metric. Commutators of fractional Laplacian has been studied mainly by Fourier
analysis. On the other hand, Fourier analysis is not sufficient to consider the commutator
estimate with rough metric. In this talk, we consider the commutator estimate by combining spectrum analysis and Fourier analysis. This talk is based on a joint work with
Luigi Forcella, Professors Vladimir Georgiev and Tohru Ozawa ( arXiv:1804.02524).

8. A sufficient and necessary condition for blow-up of non-gauge invariant nonlinear periodic Schrödinger equations Invited

Kazumasa Fujiwara

2020.10.24

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech

9. A remark on blowup for weakly coupled heat systems by an ODE approach International conference

Kazumasa FUJIWARA

EDP e DINTORNI  2017.12

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Language：English   Presentation type：Oral presentation (general)

Venue：Bari University

This talk is based on a joint work with M. Ikeda and Y. Wakasugi

10. A commutator estimate of fractional Laplacian with rough coefficients and its application International conference

Kazumasa FUJIWARA

Harmonic Analysis and Nonlinear Partial Differential Equations  2019.7.3

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Language：English   Presentation type：Oral presentation (general)

Venue：Research Institute for Mathematical Sciences

This work is based on a joint work with L. Forcella, V. Georgiev, and T. Ozawa. In this talk, we see a sufficient condition of rough metric and potential for a commutator estimate with fractional derivative operator perturbed by them. Moreover, we also see an application of this commutator estimate.

11. A commutator estimate for fractional Laplacians with rough metrics International conference

Kazumasa FUJIWARA

Fifth International Conference, New Trends in the Applications of Differential Equations in Sciences  2018.6

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Language：English   Presentation type：Oral presentation (general)

This talk is based on a joint work with V. Georgiev and T.Ozawa.

12. An ODE approach for blow-up of some evolution equations in Fujita subcritical case

Kazumasa FUJIWARA

大阪駅前セミナー  2017.7

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Presentation type：Oral presentation (general)

Venue：Ryukoku University

This talk is based on a joint work with T. Ozawa and that with M. Ikeda and Y. Wakasugi.

13. Kazumasa FUJIWARA

2019.7.20

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Language：Japanese   Presentation type：Oral presentation (general)

Venue：Advanced Mathematical Institute, Osaka City University

14. On the blow-up phenomena for derivative type nonlinear Schr?dinger euqations on torus

Kazumasa FUJIWARA

平成29年度育志賞研究発表会,  2017.9

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Presentation type：Oral presentation (general)

Venue：Osaka University

This talk is based on a joint work with T. Ozawa.

15. Remark on blow-up for the half Ginzburg-LandauKuramoto equation with rough coefficients International conference

Kazumasa FUJIWARA

12th ISAAC Congress  2019.8.2

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Language：English   Presentation type：Oral presentation (general)

Venue：University of Aveiro

In this talk, we study the blow-up for solutions to the half Ginzburg-Landau-Kuramoto equation with an ode argument The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric.

File： schedule.pdf

16. On self-similar solutions to the derivative nonlinear Schr\"odinger equation International conference

Kazumasa FUJIWARA

PDE Workshop Waseda - GSSI, L'Aquila-Pisa, Universit? di Pisa  2019.2

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Language：English   Presentation type：Oral presentation (general)

Venue：Pisa University

This talk is based on a joint work with V. Georgiev and T.Ozawa.

17. On self-similar solutions to the derivative nonlinear Schr?dinger equation

Kazumasa FUJIWARA

応用数理解析セミナー  2019.4

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Presentation type：Oral presentation (general)

Venue：Touhoku University

This talk is based on a joint work with V. Georgiev and T.Ozawa.

18. Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and metric Invited International conference

Kazumasa FUJIWARA

The 45th Conference Applications of Mathematics in Engineering and Economics  2019.6

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Language：English   Presentation type：Oral presentation (general)

Venue：Sozopol

This talk is based on a joint work with L. Forcella, V. Georgiev, and T.Ozawa.

File： programAMEE19.pdf

19. Lifespan of strong solutions to the periodic nonlinear Schr?dinger equation without gauge invariance International conference

Kazumasa FUJIWARA

International Workshop on “Fundamental Problems in Mathematical and Theoretical Physics”  2017.8

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Language：English   Presentation type：Oral presentation (general)

Venue：Waseda University

20. Higher order fractional Leibniz estimates International conference

Kazumasa FUJIWARA

ISAAC Congress 2017  2017.8

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Language：English   Presentation type：Oral presentation (general)

Venue：Linn?us University

This talk is based on a joint work with V. Georgiev and T.Ozawa.

21. Blow-up for self-interacting fractional Ginzburg-Landau equation and related commutator estimates

Kazumasa FUJIWARA

熊本大学応用解析セミナー  2017.4

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Presentation type：Oral presentation (general)

Venue：Kumamoto University

This talk is based on a joint work with V. Georgiev and T. Ozawa.

22. Blow-up for self-interacting fractional Ginzburg-Landau equation

Kazumasa FUJIWARA

第 24 回応用解析研究会シンポジウム  2017.3

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Presentation type：Oral presentation (general)

Venue：Hakone

This talk is based on a joint work with V. Georgiev and T. Ozawa.

23. Blow-up for self-interacting fractional Ginzburg-Landau equation

Kazumasa FUJIWARA

第1回中央大学偏微分方程式セミナー  2017.4

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Presentation type：Oral presentation (general)

Venue：Chuo University

This talk is based on a joint work with V. Georgiev and T. Ozawa.

24. An ODE approach for the blow-up for nonlinear damped wave equations with time dependent damping

Kazumasa FUJIWARA

なかもず解析セミナー  2017.9

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Presentation type：Oral presentation (general)

Venue：Osaka Prefecture University

This talk is based on a joint work with M. Ikeda and Y. Wakasugi.

### KAKENHI (Grants-in-Aid for Scientific Research) 4

1. Grant number：20K14337  2020.4 - 2023.3

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

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Authorship：Principal investigator

Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）

2. Study on the blowup phenomena for partial differential equations with non-gage invariant powertype nonlinearity

2019.4 - 2022.3

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

Kazumasa FUJIWARA

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Authorship：Principal investigator  Grant type：Competitive

Grant amount：\9360000 （ Direct Cost: \7200000 、 Indirect Cost：\2160000 ）

3. Mathematical basis of semirelativistic field

2016.4 - 2018.3

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

Kazumasa FUJIWARA

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Authorship：Principal investigator  Grant type：Competitive

Grant amount：\17000000 （ Direct Cost: \17000000 ）

4. Study onthe Caucy problem of semirelativistic equations with powretype nolinearity and related inequalities

2014.4 - 2017.3

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

Kazumasa FUJIWARA

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Authorship：Principal investigator  Grant type：Competitive

Grant amount：\2800000 （ Direct Cost: \2800000 ）

### Teaching Experience (Off-campus) 4

1. Exercise in Mathematics II

2021.10 - 2022.2 School of Science, Nagoya University, Department of Mathematics）

2. Exercise in Mathematics I

2021.4 - 2021.8 Nagoya University）

3. 数学演習A

2017.4 - 2017.8 中央大学 理工学部 数学科）

4. Pysics II(b)

2012.9 - 2013.3

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Level：Other  Country：Japan

### Social Contribution 1

1. The contents of mathematical library

Role(s)：Lecturer

Graduate School of Mathematics, Nagoya University  2021.8