Name

KOZONO, Hideo

Official Title

Professor

Affiliation

(School of Fundamental Science and Engineering)

Contact Information

URL

Grant-in-aids for Scientific Researcher Number
00195728

Sub-affiliation

Sub-affiliation

Faculty of Science and Engineering(Graduate School of Fundamental Science and Engineering)

Affiliated Institutes

流体数学研究所

研究所員 2015-

熱エネルギー変換工学・数学融合研究所

研究所員 2017-

理工学術院総合研究所(理工学研究所)

兼任研究員 2018-

Career

1991/08-1991/09Paderborn university
1995/10-1996/03Bonn university
2003/04-2003/09Paderborn University
2008/06-2008/07Darmstadt 工科大学

Paper

Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system

Kozono, Hideo;Sugiyama, Yoshie;Yahagi, Yumi

JOURNAL OF DIFFERENTIAL EQUATIONS 253(7) p.2295 - 23132012-2012

DOIWoS

Detail

ISSN:0022-0396

On the stationary Navier-Stokes equations in exterior domains

Kim, Hyunseok;Kozono, Hideo

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 395(2) p.486 - 4952012-2012

DOIWoS

Detail

ISSN:0022-247X

Global Compensated Compactness Theorem for General Differential Operators of First Order

Kozono, Hideo;Yanagisawa, Taku

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 207(3) p.879 - 9052013-2013

DOIWoS

Detail

ISSN:0003-9527

Hadamard Variational Formula for the Green's Function of the Boundary Value Problem on the Stokes Equations

Kozono, Hideo;Ushikoshi, Erika

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 208(3) p.1005 - 10552013-2013

DOIWoS

Detail

ISSN:0003-9527

Weak solutions of the stationary Navier-Stokes equations for a viscous incompressible fluid past an obstacle

Heck, Horst;Kim, Hyunseok;Kozono, Hideo

MATHEMATISCHE ANNALEN 356(2) p.653 - 6812013-2013

DOIWoS

Detail

ISSN:0025-5831

Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems

Kozono, Hideo;Yanagisawa, Taku

MANUSCRIPTA MATHEMATICA 141(3-4) p.637 - 6622013-2013

DOIWoS

Detail

ISSN:0025-2611

Remark on the stability of the large stationary solutions to the Navier-Stokes equations under the general flux condition

Kanbayashi, Naoya;Kozono, Hideo;Okabe, Takahiro

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 409(1) p.378 - 3922014-2014

DOIWoS

Detail

ISSN:0022-247X

Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality

Farwig, Reinhard;Kozono, Hideo

JOURNAL OF DIFFERENTIAL EQUATIONS 256(7) p.2633 - 26582014-2014

DOIWoS

Detail

ISSN:0022-0396

Existence of periodic solutions and their asymptotic stability to the Navier-Stokes equations with the Coriolis force

Kozono, Hideo;Mashiko, Yuki;Takada, Ryo

JOURNAL OF EVOLUTION EQUATIONS 14(3) p.565 - 6012014-2014

DOIWoS

Detail

ISSN:1424-3199

A remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions

Kozono, Hideo;Terasawa, Yutaka;Wakasugi, Yuta

JOURNAL OF FUNCTIONAL ANALYSIS 272(2) p.804 - 8182017-2017

DOIWoS

Detail

ISSN:0022-1236

Leray's problem on $D$-solutions to the stationary Navier-Stokes equations past an obstacle (Mathematical Analysis of Incompressible Flow)

Heck Horst;Kim Hyunseok;KOZONO Hideo

RIMS Kokyuroku 1875p.19 - 282014/01-2014/01

CiNii

Detail

ISSN:1880-2818

Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid

Kozono, Hideo; Miura, Masanari; Sugiyama, Yoshie

Journal of Functional Analysis 270(5) p.1663 - 16832016/03-2016/03

DOIScopus

Detail

ISSN:00221236

Outline:© 2015 Elsevier Inc..We consider the Keller-Segel system coupled with the Navier-Stokes fluid in the whole space, and prove the existence of global mild solutions with the small initial data in the scaling invariant space. Our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data. As a byproduct, we show the asymptotic stability of solutions as the time goes to infinity. Since we may deal with the initial data in the weak Lp-spaces, the existence of self-similar solutions provided the initial data are small homogeneous functions.

Hadamard variational formula for eigenvalues of the Stokes equations and its application

Jimbo, Shuichi; Kozono, Hideo; Teramoto, Yoshiaki; Ushikoshi, Erika

Mathematische Annalen 368(1-2) p.877 - 8842017/06-2017/06

DOIScopus

Detail

ISSN:00255831

Outline:© 2016, Springer-Verlag Berlin Heidelberg. Based on the explicit representation of the Hadamard variational formula [1] for eigenvalues of the Stokes equations, we investigate the geometry of the domain in R 3 . It turns out that if the first variation of some eigenvalue of the Stokes equations for all volume preserving perturbations vanishes, then the domain is necessarily diffeomorphic to the 2-dimensional torus T 2 .

Asymptotic behavior of radially symmetric solutions for a quasilinear hyperbolic fluid model in higher dimensions

Hashimoto, Itsuko; Kozono, Hideo

Journal of Differential Equations 262(10) p.5133 - 51592017/05-2017/05

DOIScopus

Detail

ISSN:00220396

Outline:© 2017 Elsevier Inc. We consider the large time behavior of the radially symmetric solution to the equation for a quasilinear hyperbolic model in the exterior domain of a ball in general space dimensions. In the previous paper [2], we proved the asymptotic stability of the stationary wave of the Burgers equations in the same exterior domain when the solution is also radially symmetric. On the other hand, in the 1D-case, a similar asymptotic structure as above to the damped wave equation with a convection term has been established by Ueda [10] and Ueda–Kawashima [11]. Assuming a certain condition on the boundary data on the ball and the behavior at infinity of the fluid, we shall prove that the stationary wave of our quasilinear hyperbolic model is asymptotically stable. The weighted L 2 -energy method plays a crucial role in removing such a restriction on the sub-characteristic condition on the stationary wave.

Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

Farwig, Reinhard; Kozono, Hideo; Wegmann, David

Journal of Mathematical Analysis and Applications 453(1) p.271 - 2862017/09-2017/09

DOIScopus

Detail

ISSN:0022247X

Outline:© 2017 Elsevier Inc. Recently, Leray's problem of the L 2 -decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.

Research Grants & Projects

Grant-in-aids for Scientific Research Adoption Situation

Research Classification:

New development of the theory on turbulence via method of nonlinear partial differential equations

2012/-0-2015/-0

Allocation Class:¥3900000

Research Classification:

Geometric properties and asymptotic behavior of solutions of diffusion equations

2011/-0-2015/-0

Allocation Class:¥17680000

Research Classification:

Theory of global well-posedness on the nonlinear partial differential equations

2008/-0-2013/-0

Allocation Class:¥146120000

Research Classification:

Harmonic analysis by real variable methods and its applications

Allocation Class:¥15130000

Research Classification:

Studies on construction of solutions of nonlinear elliptic equations arising from Gaugetheories and on the asymptotic behavior of their heat flows

Allocation Class:¥3670000

Research Classification:

Reseach for the singularities and regularity of solutions to crtical nonlinear partial differential equations

Allocation Class:¥12900000

Research Classification:

Structure of Solutions and Geometric Symmetry for Nonlinear Evolution Equations

Allocation Class:¥40430000

Research Classification:

Asymptotic behavior of solutions for some diffusive equations and its applications

Allocation Class:¥3500000

Research Classification:

United theory of existence of global solution and its asymptotic behavior to the nonlinear partial differential equations

Allocation Class:¥79300000

Research Classification:

Applied Analysis for Nonlinear Systems

Allocation Class:¥12100000

Research Classification:

Autonomous Formation of Spatial Structures in Solutions of Parabolic Partial Differential Equations

Allocation Class:¥14500000

Research Classification:

Geometric invariant, propagation of singularity and asymptotic behavior for nonlinear wave equations

Allocation Class:¥11200000

Research Classification:

Research on a refinement of the energy inequality for weak solutions to the Navier-Stokes equations

Allocation Class:¥3500000

Research Classification:

Asymptotic Analysis for Singularities of Solutions to Nonlinear Partial Differential Equations

1999-2002

Allocation Class:¥13900000

Research Classification:

Variational Problems in Differential Geometry

1997-1999

Allocation Class:¥14300000

Research Classification:

Spectral and Scattering Theory for Schrodinger Operators

1997-2000

Allocation Class:¥13600000

Research Classification:

Research on well-posedness for the Navier-Stokes equations

1997-2000

Allocation Class:¥13600000

Research Classification:

Development and verification of analytical and statistical theory of turbulence

1997-1998

Allocation Class:¥7700000

Research Classification:

Research for the Lp theory of the solutions to nonlinear partial differential equations

1997-1998

Allocation Class:¥3100000

Research Classification:

New development of mathematical theory of turbulence by collaboration of the nonlinear analysis and computational fluid dynamics

2016/-0-2021/-0

Allocation Class:¥160680000

Research Classification:

Research of Navier-Stokes equations in undounded domains by real analysis and the energy method

2013/-0-2017/-0

Allocation Class:¥4810000

Research Classification:

Modern Mathematical Analysis for the Fluid Dynamics

2019/-0-2023/-0

Allocation Class:¥17680000

On-campus Research System

Special Research Project

現代解析学の手法による乱流理論の研究

2012

Research Results Outline:1. 回転する障害物の周りの定常Navier-Stokes 方程式の解の存在と一意性3次元空間において障害物が回転し,かつ回転軸と同じ方向に並進運動す1. 回転する障害物の周りの定常Navier-Stokes 方程式の解の存在と一意性3次元空間において障害物が回転し,かつ回転軸と同じ方向に並進運動する場合に,その外部領域 $\Omega$ において非圧縮性粘性流体のNavier-Stokes 方...1. 回転する障害物の周りの定常Navier-Stokes 方程式の解の存在と一意性3次元空間において障害物が回転し,かつ回転軸と同じ方向に並進運動する場合に,その外部領域 $\Omega$ において非圧縮性粘性流体のNavier-Stokes 方程式の定常解の存在と一意性を考察した.実際,回転の角速度を$\omega$,並進速度を$u_{\infty}$かつ外力$f = \dive F$ が条件$|\omega| + |u_{\infty}| + \|F\|_{L^{\frac32, \infty}} << 1$ であれば,$\nabla u \in L^{\frac32, \infty}(\Omega)$ であって,$u\in L^{3,\infty}(\Omega)$ である小さい解 $u$ が一意的に存在することを証明した.より一般的な一意性定理として,与えられデータ$\omega\in \re^3$, $u_{\infty}\in \re^3$, $F \in L^{\frac32,\infty}(\Omega)$ が十分小さく,かつ$F\in L^{\frac32,\infty}(\Omega) \cap L^{q,\infty}(\Omega)$, $3/2 < r < 3$ であれば,我々の構成した解 $u$ は$\nabla u \in L^{\frac32,\infty}(\Omega) \cap L^{q,\infty}(\Omega)$ なるクラスで一意的であることを証明した.さらに,これらのデータが小さい限りにおいては,データーに関する解の連続依存性が成立する.2. 外部領域における定常Navier-Stokes 方程式の弱解の一意性とエネルギー不等式の関係3次元外部領域$\Omega$においては,Leray により任意の外力$\dive F$, $F\in L^2(\Omega)$ に対して,$\nabla u\in L^2(\Omega)$ でエネルギー不等式 $\|\nabla u\|^2_{L^2(\Omega)} \le \dis{-\int_{\Omega}F\cdot\nabla u}dx$を満たす弱解 $u$ の存在が示されている.しかし,そのような弱解については,空間 $L^{3, \infty}(\Omega)$ における小ささを仮定する必要があった.本研究では,弱解そのものに対する小ささではなく,与えられた外力$F\in L^2(\Omega)\cap L^{\frac32,\infty}(\Omega)$ が空間$L^{\frac32,\infty}(\Omega)$ において十分小さければ,$\nabla u \in L^2(\Omega)$ であってエネルギー不等式を満たす弱解$u$ は一意的に存在することを証明した.この結果は期待できる定常Navier-Stokes 方程式の弱解の存在と一意性に関しては,最良の結果と言える.

非線形偏微分方程式の大域的理論の新展開

2013

Research Results Outline:(i) 一般領域におけるStoeks 作用素の最大正則性Stokes 作用素のq-乗可積分空間理論はq=2 の場合を除き、一般の領域では定義が出来ない(i) 一般領域におけるStoeks 作用素の最大正則性Stokes 作用素のq-乗可積分空間理論はq=2 の場合を除き、一般の領域では定義が出来ないことが知られている。そこで、反例が構成されている非コンパクトな境界をもつn 次元空間内の非有界領域...(i) 一般領域におけるStoeks 作用素の最大正則性Stokes 作用素のq-乗可積分空間理論はq=2 の場合を除き、一般の領域では定義が出来ないことが知られている。そこで、反例が構成されている非コンパクトな境界をもつn 次元空間内の非有界領域を取り扱った。通常のq-乗可積分空間に代わるものとして、2乗可積分空間とq-乗可積分指数の和および共通部分からなる関数空間を導入した。これらの関数空間はともに、関数自身の無限遠方では減衰の速度が2乗可積分関数と同程度であることを要請したものである。その結果、領域の境界が一様にC1-級であれば、非コンパクト領域においてもStokes 作用素はこれらの関数空間において定義可能であり、正則半群を生成するとともに最大正則性定理を満たすことが明らかにされた。(ii) Navier-Stokes 方程式の弱解の正則性に関する新たな指標3次元有界領域におけるNavier-Stokes 方程式の弱解で強エネルギー不等式満たすクラスの正則性を考察した。従来はSerrin によって提唱された時空間におけるスケール不変な可積分空間において正則性の指標が確立されていたが、本研究では運動エネルギーとエネルギー散逸量に着目した。すなわち、前者に対しては指数が1/2 より大きな時間変数のヘルダー連続関数であり、また後者に対しては積分量の時間爆発レートが-1/2 より遅ければ、弱解が滑らかであることを証明した。これら2つの指標は、時空間の関数のセミノルムと見なすとき、スケール変換則に関して不変であることに注意が必要である。

Lecture Course

Course TitleSchoolYearTerm
Vector AnalysisSchool of Fundamental Science and Engineering2019full year
Vector Analysis [S Grade]School of Fundamental Science and Engineering2019full year
Seminar in Mathematics ASchool of Fundamental Science and Engineering2019spring semester
Seminar in Mathematics A [S Grade]School of Fundamental Science and Engineering2019spring semester
Seminar in Mathematics BSchool of Fundamental Science and Engineering2019fall semester
Seminar in Mathematics B [S Grade]School of Fundamental Science and Engineering2019fall semester
Functional Analysis ASchool of Fundamental Science and Engineering2019full year
Functional Analysis ASchool of Fundamental Science and Engineering2019full year
Special Exercise on MathematicsSchool of Fundamental Science and Engineering2019fall semester
Supplementary Seminar in Mathematics ASchool of Fundamental Science and Engineering2019spring semester
Supplementary Seminar in Mathematics BSchool of Fundamental Science and Engineering2019fall semester
Undergraduate ResearchSchool of Fundamental Science and Engineering2019full year
Seminar in Applied Mathematics ASchool of Fundamental Science and Engineering2019spring semester
Seminar in Applied Mathematics A [S Grade]School of Fundamental Science and Engineering2019spring semester
Seminar in Applied Mathematics BSchool of Fundamental Science and Engineering2019fall semester
Seminar in Applied Mathematics B [S Grade]School of Fundamental Science and Engineering2019fall semester
Research Project BSchool of Fundamental Science and Engineering2019spring semester
Research Project B [S Grade]School of Fundamental Science and Engineering2019spring semester
Research Project CSchool of Fundamental Science and Engineering2019fall semester
Research Project C [S Grade]School of Fundamental Science and Engineering2019fall semester
Advanced AnalysisSchool of Fundamental Science and Engineering2019spring semester
Research Project ASchool of Fundamental Science and Engineering2019fall semester
Research Project DSchool of Fundamental Science and Engineering2019spring semester
Master's Thesis (Department of Pure and Applied Mathematics)Graduate School of Fundamental Science and Engineering2019full year
Research on Functional Analysis and Non-linear Partial Differential EquationsGraduate School of Fundamental Science and Engineering2019full year
Research on Functional Analysis and Non-linear Partial Differential EquationsGraduate School of Fundamental Science and Engineering2019full year
Seminar on Functional Analysis and Non-linear Partial Differential Equations AGraduate School of Fundamental Science and Engineering2019spring semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations AGraduate School of Fundamental Science and Engineering2019spring semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations BGraduate School of Fundamental Science and Engineering2019fall semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations BGraduate School of Fundamental Science and Engineering2019fall semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations CGraduate School of Fundamental Science and Engineering2019spring semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations CGraduate School of Fundamental Science and Engineering2019spring semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations DGraduate School of Fundamental Science and Engineering2019fall semester
Seminar on Functional Analysis and Non-linear Partial Differential Equations DGraduate School of Fundamental Science and Engineering2019fall semester
Master's Thesis (Department of Pure and Applied Mathematics)Graduate School of Fundamental Science and Engineering2019full year
Foundations of Mathematical Analysis 1Graduate School of Fundamental Science and Engineering2019spring semester
Foundations of Mathematical Analysis 1Graduate School of Fundamental Science and Engineering2019spring semester
Foundations of Mathematical Analysis 1Graduate School of Creative Science and Engineering2019spring semester
Foundations of Mathematical Analysis 1Graduate School of Creative Science and Engineering2019spring semester
Foundations of Mathematical Analysis 1Graduate School of Advanced Science and Engineering2019spring semester
Foundations of Mathematical Analysis 1Graduate School of Advanced Science and Engineering2019spring semester
Research on Functional Analysis and Non-linear Partial Differential EquationsGraduate School of Fundamental Science and Engineering2019full year
Special Lecture on Mathematical Fluid MechanicsGraduate School of Fundamental Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Fundamental Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Fundamental Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Creative Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Creative Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Advanced Science and Engineering2019an intensive course(spring and fall)
Special Lecture on Mathematical Fluid MechanicsGraduate School of Advanced Science and Engineering2019an intensive course(spring and fall)