Curriculum vitae

 

Tsuyoshi Yoneda

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                               

 


                                                                                    Photo by Pawel Konieczny.

 

 

 





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http://www.youtube.com/watch?v=1BzYg6ly0ZY

http://www.youtube.com/watch?v=ymolZXMRmVg

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Sapporo city life
http://www.youtube.com/watch?v=79zmRPxO-wI
Manhattan city life
http://www.youtube.com/watch?v=v_qpk84SAV8
Total drama action in Times Square
http://www.youtube.com/watch?v=6osM5O7ZrpU

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Research interest: Navier-Stokes equation
 

A regularity criteriton in a supercritical space:


Modern regularity theory for solutions to the 3D Navier-Stokes equation (NS) began with the works of Leray (1934) and Hopf (1951). After the fundamental works of Leray and Hopf, progress in addressing the full regularity of Leray-Hopf solutions has been very slow. One of the significant progress was made by Prodi (1959), Serrin (1963) and Ladyzhenskaya (1967). After the appearance of the Prodi-Serrin-Ladyzhenskaya criterion, many different regularity criteria of solutions to NS was established by many researchers working in the regularity theory of NS. The main idea in the NS regularity field is to use scaling invariant (critical) function spaces. Thus, our first aim was to construct a regularity criterion in a supercritical function space (with an additional condition), and then succeeded to construct it in terms of some exponential control on the rate of change of ``some value" along streamlines in a supercritical function space (Chan-Y, MAA, 2012). After constructed the theorem, we realized two things:


1. The differential geometric consideration along streamlines (characteristic curve) is very important idea, but not so many work in NS field.


2. We need to analyze the pressure term more and more, but up to now, it has been very slow. The pressure is expressed by using ``singular integral". However it is not so easy to extract a local information of the pressure due to the singular integral. Nevertheless, some researchers have been trying to extract a local information (more or less) from the singular integral. Recently, Bourgain and Li (arXiv:1307.7090) showed ill-posedness of the incompressible Euler equation in borderline Sobolev spaces. They extract a local information (more or less) of the vorticity from the singular integral. Rigorously, they considered vorticity equations and in this case, the velocity is expressed in the singular integral. See also arXiv 1310.4799 (Kiselev and Sverak).


A new type of blowup criterion:


In the first (1 in the above) point of view, we constructed a new type of blowup criteria in terms of pseudo locality near maximum points. In this work, we define ``local collapsing scenario" and ``local non-collapsing scenario" in a geometric sense (the word ``pseudo locality" and ``local collapsing" come from Ricci flow study field). Such ``local collapsing scenario” concept arises from the second (2 in the above) point of view, namely, ``singular integral".  Roughly saying, if the solution is ``local non-collapsing" at maximum points, then the solution never blowup. So, our main purpose is to analyze local collapsing scenario. To see the scenario deeply, a lot of numerical simulations (joint work with Prof. Notsu) must be useful. In the numerical computation, we observe that swirling streamlines structure may have ``binding maximum effect" to the corresponding axis. This observation  is closely related to ``Burgers vortex" and ``vortex tube".


Also we are trying to collaborate with turbulence analyst (with Prof. Saiki).


Separation phenomena:


In order to progress the local collapsing scenario along maximum points, analyzing ``separation phenomena" is one of the important direction. In general, before separating from a boundary, the flow moves toward reverse direction near the boundary against the laminar flow direction.  In ``boundary layer theory" (BLT) point of view, such phenomena itself is well studied. Our main purpose is to just progress ``local pressure analysis method" through (well-known) separation phenomena.


In the beginning of 20th century, Prandtl proposed BLT, and it has been developing extensively. See Rosenhead (1963) for example. Basically, BLT equation can be deduced from the Navier-Stokes equation. Van Dommelen and Shen (1980) made a key observation of shock singularities from BLT equation. However, they could only give a numerical proof, since an analytical treatment was too difficult. In the beginning of 21th century,  Ghil, Ma and Wang have developed a mathematical rigorous theory on boundary layer separation of incompressible fluid flows. Their articles are oriented toward to structural bifurcation and boundary layer separation of the solution to the Navier-Stokes equations.  More precisely, they established a simple equation, which they call ``separation equation" linking the separation location and times. Furthermore they showed that the structural bifurcation occurs at a degenerate singular point with integer index of the velocity field at the critical bifurcation time. Their theory are based on classification of the detailed orbit structure of the velocity field near the bifurcation time and location. In my study, Ghil, Liu, Wang and Wang's work (Physica D, 2004) is one of the milestone (for me). They tried to give a new rigorous argument of ``adversed pressure gradient" mathematically. The appearance of the adverse pressure gradient is well known to be the main mechanism for the boundary-layer separation in physics. They were carefully verified but still using a numerical experiment. We generalized their result to sphere and hyperbolic space with Prof. Chan and Prof. Czubak http://eprints3.math.sci.hokudai.ac.jp/2337/1/pre1047.pdf (see also http://eprints3.math.sci.hokudai.ac.jp/2295/2/pre1040.pdf), also, the compressible fluid case with Prof. Ueda.


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A list of publications (Articles in refereed journal):



[24] C-H Chan and T. Yoneda, On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space, Dynamics of PDE, 10 (2013) 209--254.


[23] S.Ibrahim and T. Yoneda, Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data, J. Math. Sci. Univ. Tokyo, 20 (2013) 1--25
 

[22]E. Foxall, S. Ibrahim and T. Yoneda, Streamlines concentration and application to the incompressible Navier-Stokes equations, Tohoku Math. J., 65 (2013) 273--279.


[21] D. Chae and T. Yoneda, On the Liouville theorem for the stationary Navier-Stokes equations in a critical space, J. Math. Anal. Appl., 405 (2013) 706--710.

 
[20]M. Yamada and T. Yoneda, Resonant interaction of Rossby waves in two-dimensional flow on a β plane,  Physica D, 245 (2013) 1--7.

 
[19]C-H. Chan and T. Yoneda, On possible isolated blow-up phenomena and regularity criterion of the 3D Navier-Stokes equation along the streamlines,  Methods and Applications of Analysis, 19 (2012) 211--242.


[18]G. Misiolek and T. Yoneda, Ill-posedness examples for the quasi-geostrophic and the Euler equations,  in Analysis, Geometry and Quantum Field Theory, Contemporary Mathematics, Amer. Math. Soc., Providence, RI, (2012) 251--258.
 

[17]S. Ibrahim and T. Yoneda, Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data, J. Math. Anal. Appl., 396 (2012) 555--561.

 
[16]H. Koba, A. Mahalov and T. Yoneda, Global well-posedness for the rotating Navier-Stokes-Boussinesq equations with stratification effects, Adv. Math. Sci.  Appl., 22 (2012) 61--90.

 
[15]E. Nakai and T. Yoneda, Bilinear estimates in dyadic BMO and the Navier-Stokes equations, J. Math. Soc. Japan, 64 (2012) 399--422.

 
[14]Y. Giga, A. Mahalov and T. Yoneda, On a bound for amplitudes of Navier-Stokes flow with almost periodic initial data, J. Math. Fluid Mech., 13 (2011) 459--467.

 
[13]E. Nakai and T. Yoneda, Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations, Hokkaido Math. J., 40 (2011) 67--88.

 
[12]P. Konieczny and T. Yoneda, On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations, J. Diff. Eq., 250 (2011) 3859--3873.

 
[11]T. Yoneda, Long-time solvability of the Navier-Stokes equations in a rotating frame with spatially almost periodic large data, Arch. Ration. Mech. Anal., 200 (2011) 225--237.

 
[10]Y. Taniuchi, T. Tashiro and T. Yoneda, On the two-dimensional Euler equations with spatially almost periodic initial data, J. Math. Fluid Mech., 12 (2010) 594--612.

 
[9]T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near BMO^{-1}, J. Funct. Anal., 258 (2010) 3376--3387.

 
[8]E. Nakai and T. Yoneda, Construction of solutions for the initial value problem of a functional-differential equation of advanced type, Aeq. Math., 77 (2009) 259 -- 272.

 
[7]Y. Giga, H. Jo, A. Mahalov and T. Yoneda, On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data, Physica D, 237 (2008) 1422--1428.

 
[6]Y. Sawano and T. Yoneda, Quarkonial decomposition suitable for functional-differential equations of delay type, Math. Nachr., 281 (2008) 1810--1822.

 
[5]N. Kikuchi, E. Nakai, N. Tomita, K. Yabuta and T. Yoneda, Calderon-Zygmund operators on amalgam spaces and in the discrete case, J. Math. Anal. Appl., 335 (2007) 198--212.

 
[4]Y. Sawano and T. Yoneda, On the Young theorem for amalgams and Besov spaces, Int. J. Pure Appl. Math., 36 (2007) 199--208.

 
[3]T. Yoneda, On the functional-differential equation of advanced type f'(x)=af(λx), λ>1, with f(0)=0, J. Math. Anal. Appl., 332 (2007) 487--496.

 
[2]T. Yoneda, On the functional-differential equation of advanced type f'(x)=af(2x) with f(0)=0, J. Math. Anal. Appl., 317 (2006) 320--330.

 
[1]T. Yoneda, Spline functions and n-periodic points (Japanese), Trans. Japan Soc. Ind.  Appl. Math., 15 (2005) 245--252.




査読付きジャーナルへ投稿中の論文
 

[25]T. Yoneda, A Mathematical clue to the separation phenomena on the two-dimensional Navier-Stokes equation.

 

[26] T. Yoneda, Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions.


[27]C-H. Chan, M. Czubak and T. Yoneda, An ODE for boundary layer separation on a sphere and a hyperbolic space .


 

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Honors:


 

JSPS Research Fellowship for Young Scientists(学振特別研究員DC1): April 2006--March 2009, at University of Tokyo.


 

Chairman Award for Outstanding Ingenuity and Creativity(数理科学研究科長賞), University of Tokyo, March 2009.


 

Postdoctoral Fellowship Award, Institute for Mathematics and its Applications September 2009-August 2011


 

Postdoctoral Fellowship Award,  Pacific Institute for the Mathematical Sciences September 2010-August 2012


 

Inoue Research Award for Young Scientists(井上研究奨励賞)February 2012.


 

MSJ Tatebe Katahiro Prize(日本数学会賞:建部賢弘特別賞)September 2012.


 

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Selected Invited Talks:



A differential geometric consideration on the Navier-Stokes flow and its numerical computation, Mathematical Theory of Turbulence via Harmonic Analysis and Computational Fluid Dynamics, Hotel Nikko Nara, Japan, March 2014



A differential geometric consideration on the Navier-Stokes flow, 第3 回弘前非線形方程式研究会, Hirosaki Univ., Aomori, Nov. 2013


A differential geometric consideration on the Navier-Stokes flow and its numerical computation, The analysis seminar, Binghamton Univ., New York, Nov. 2013



Navier-Stokes方程式に対する微分幾何学的考察について, 幾何学コロキウム, Hokkaido Univ. Oct. 2013

 


Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions, Fourth Japan-China Workshop on Mathematical Topics from Fluid Mechanics, Tokyo tech Univ., Sep. 2013



Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions, 第2回岐阜数理科学研究会, Takayama, Gifu, Sep. 2013


 


Local behaviors of the Navier-Stokes flow:swirling streamline and shear flow, 「第9回非線型の諸問題」, Kochi Univ. Sep. 2013


 

Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions, RIMS 研究集会(調和解析と偏微分方程式)京都大学数理解析研究所, July. 2013.


 

Topological Instability of Laminar Flows for the Two-dimensional Navier-Stokes Equation with Circular Arc No-slip Boundary Conditions, PRIMA Congress Shanghai, China, June 2013.


 

フーリエ解析と回転場内のNavier--Stokes方程式について,Fourier analysis and rotating Navier--Stokes equations, 日本数学会年会・実函数論分科会における特別講演, Kyoto Univ., Mar. 2013


 

Mathematical consideration of separation phenomena on the
two-dimensional Navier-Stokes equation, seminar, Chung-Ang Univ. Korea, March 2013.


 

On two approaches to Navier-Stokes problems: frequency analysis and geometric analysis, Oberwolfach Workshop (Geophysical Fluid Dynamics), Oberwolfach, Germany, February 2013.


 

A Mathematical clue to the separation phenomena on the two-dimensional Navier-Stokes equation, RIMS 研究集会(非圧縮流の数理解析)京都大学数理解析研究所, Feb. 2013.


 

実解析研究と流体方程式研究におけるbrainstormingの提案, 調和解析セミナー, The University of Tokyo, December 2012.



A Mathematical clue to the separation phenomena on the two-dimensional Navier-Stokes equation, Harmonic Analysis and its Applications at Tokyo 2012, Tokyo Metropolitan University, November 2012.



2次元Navier-Stokes方程式による剥離現象の数学的考察について, Kobe Analysis seminar, Kobe University, June 2012, invited by Y. Maekawa.


 

様々な惑星に存在する帯状流の純粋数学による定式化、及びそれに関連する話題につ いて, 解析セミナー,  Ibaraki University, January 2012, invited by E. Nakai.


 

Long time solvability of equations in geophysical fluid dynamics, 「若手による流体力学の基礎方程式研究集会」, Nagoya University, January 2012.


 

Long time solvability of equations in geophysical fluid dynamics,  Differential Equations and their Applications -- Sino-Japan Conference of Young Mathematicians, Nankai University in Tianjin, China, December, 2011.


 


様々な惑星に存在する帯状流の純粋数学による定式化、及びそれに関連する話題について
On the mathematical analysis of the zonal flow and related topics, NLPDE seminar, Kyoto University, December 2011, invited by Y. Sawano.


 

T. Yoneda, Long time solvability of equations in geophysical fluid dynamics, SIAM
Conference on Analysis of Partial Differential Equations, San Diego, California, USA,
November 2011.


T. Yoneda, On a generalized Bernoulli principle for the incompressible Euler equations,
mathematics colloquium, Sungkyunkwan University, Korea, September 2011, invited by D. Chae.


T. Yoneda,応用解析学研究T(集中講義)大阪教育大学, 2011 年8 月2 日から5 日まで


T. Yoneda, Global solvability of the rotating Navier-Stokes equations and related
topics, Minisymposium of ICIAM 2011, Recent topics on mathematical analysis for the
Navier-Stokes equations, Vancouver, Canada, July 2011.


T. Yoneda, Long time solvability of the Navier-Stokes-Boussinesq equations and related
topics, 2011 ICIAM Satellite Meetings, Workshop on Applied Analysis and Applied PDEs,
University of Victoria, Canada, July 2011.


 


(ヴィクトリア大PIMSポスドク時代)


 


T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equation and related topics,
Differential Geometry-Mathematical Physics-Partial Differential Equations Seminars, The
University of British Columbia, Canada, October 2010, invited by S. Gustafson.


 


(ミネソタ大IMAポスドク時代)


 


T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations near BMO^{-1}, Sapporo
symposium, Hokkaido University, August 2010.


T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations, BIBUNHOUTEISHIKI seminar,
Osaka University, July 2010, invited by H. Miura.


T. Yoneda, Long-time solvability of the Navier-Stokes equations in a rotating frame with
spatially almost periodic large data, IRTG Seminar, Darmstadt University of Technology,
Germany, June 2010, invited by M. Geissert.


T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations near BMO^{-1} and its
related topics, ANALYSIS / PDE SEMINAR, Arizona State University, USA, May 2010, invited
by A. Mahalov.


T. Yoneda, Ill-posedness of the 3D-Navier-Stokes equations near BMO^{-1}, PDE,
Complex analysis and Differential Geometry Seminar, University of Notre Dame, USA, April
2010, invited by G. Misiolek.


T. Yoneda, Existence for large times of the Navier-Stokes equations in a rotating frame
with spatially almost periodic large data, Applied Mathematics Seminar, Texas Tech
University, USA, April 2010, invited by L. Hoang.


 


(成均館大学ポスドク時代)


 


T. Yoneda, Non blow-up of the Navier-Stokes equations in a rotating frame with spatially
almost periodic data, Brain Korea 21 Seminar, Ajou University, Korea, June 2009, invited
by H. O. Bae.


 


(アリゾナ州立大ポスドク時代)


 


T. Yoneda, Global solvability of the Navier-Stokes equations in a rotating frame with
spatially almost periodic data, ANALYSIS / PDE SEMINAR, Arizona State University, USA,
April 2009, invited by A. Mahalov.


 


(東大博士時代)


 


T. Yoneda, Global solvability of the Navier-Stokes equations in a rotating frame with
spatially almost periodic data, Harmonic Analysis and its Applications at Tokyo 2008, Tokyo
Metropolitan University, October 2008.


T. Yoneda, On the Navier-Stokes equations and Euler equations with spatially almost
periodic data, The International Federation of Nonlinear Analysts, Florida, USA, July 2008.




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競争的資金の獲得状況


 

JSPS Research Fellowship for Young Scientists(学振特別研究員DC1): April 2006--March 2009, at University of Tokyo.


 

Postdoctoral Fellowship Award, Institute for Mathematics and its Applications September 2009-August 2011


 

Postdoctoral Fellowship Award,  Pacific Institute for the Mathematical Sciences September 2010-August 2012


Grant-in-Aid for Young Scientists B(科研費、若手研究 B) 2013--2015

「流体方程式に対する実解析的手法および数値計算」


住友財団基礎科学研究助成 2013年11月--2014年11月

「ナヴィエ・ストークス方程式の爆発問題の解明に向けた流体乱流の大規模数値計算」
 

2013年度、北海道大学情報基盤センター共同研究実施に係る
学際大規模計算機システム利用:斉木・米田グループとして400万秒分、
スパコンのファイル容量が0.6TB分


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執筆


 

数理科学:2013年4月号サイエンス社「IMA研究所の思い出」

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Education:


 

1.  April 2004 - March 2006: Master course student at Department of Mathematics, Osaka Kyoiku University (at Osaka, Japan). Adviser: Professor Eiichi Nakai.


 

2. April 2006 - March 2009: Doctor course student at Graduate School of Mathematical Sciences, The University of Tokyo (at Tokyo, Japan).

Adviser: Professor Yoshikazu Giga.



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Employment:


 


 

1.March 2009-May 2009: Short-term scholar, Department of Mathematics, Arizona State University (at Arizona, USA)


 

2.June 2009-August 2009: The Research Doctor of the Mathematics Department at Sungkyunkwan University (at Suwon, Korea)


 

3.September 2009-August 2010: Postdoctoral fellowship, Institute for Mathematics and Its Applications (IMA), University of Minnesota (at Minnesota, USA).


 

4.September 2010--May 2011: Postdoctoral fellowship,  Pacific Institute for the Mathematical Sciences (PIMS), University of Victoria (at Victoria, Canada).


 

5.July 2011--March 2014: Assistant professor, Department of Mathematics, Hokkaido University (at Sapporo, Japan)

(北海道大学大学院理学研究院数学部門 助教 〒060-0810 札幌市北区北10条西8丁目)

 

6.April 2014--present: Assosiate professor, Department of Mathematics, Tokyo Institute of Technology

(at Tokyo, Japan)

(東京工業大学 大学院理工学研究科 数学専攻〒152-8551 東京都目黒区大岡山 2-12-1)


 

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Work Experience:


 

Teaching Assistant: April 2006- July 2006, at University of Tokyo.


 

Instructor: Fall semester 2010, Math151 (Probability), at University of Victoria.


 

北海道大学数学教室における


 

PDEセミナー世話人,2011年後期〜現在

理数応援プロジェクト委員2011

親和会委員2012--2013

広報委員2013


 

平成25年度:専門調査員(科学技術動向研究センター, 科学技術政策研究所, 文部科学省) 



応用解析学研究T(集中講義)大阪教育大学, 2011年8月2日から5日まで

線形代数学U北海道大学2011年後期

微分積分学T北海道大学2012年前期

基礎数学演習C,2012年前期

解析学B(常微分方程式論)2012年後期

微分積分学T,2013年前期

基礎数学演習C,2013年前期

科学技術の世界(数学のたのしみ),(1/4コマ)2013年前期

解析学G(フーリエ解析学)2013年後期


 


 

2013年度、修士論文:

 

石田啓明「軸対称流における3次元Navier-Stokes方程式の数値プログラミング」

 

2013年度、卒業研究


白石 光平 「オイラーの運動方程式とベルヌーイの定理について」

岩本 佳保里「スカラー場とベクトル場について」

小林 琢久生「ヒルベルト空間のスペクトルについて」

 

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https://m.math.sci.hokudai.ac.jp/webmail/
https://am.ms.u-tokyo.ac.jp/

https://webmail.ima.umn.edu/
https://mail.uvic.ca/
https://m.zaq.ne.jp/
https://hptool.zaq.ne.jp/net/htdocs/zaq/wsc/01/1.0_menu.html
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http://www.youtube.com/watch?v=XkSlFkdTDlc&feature=youtu.be