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Research Output 1985 2019

  • 2095 Citations
  • 27 h-Index
  • 87 Article
  • 4 Chapter
  • 1 Conference contribution
  • 1 Editorial
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Article
2019

A Characterization of Harmonic Lr -Vector Fields in Two-Dimensional Exterior Domains

Hieber, M. G., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2019 Jan 1, In : Journal of Geometric Analysis.

Research output: Contribution to journalArticle

Exterior Domain
Vector Field
Harmonic
Unit normal vector
Simple Closed Curve
Blow-up Criterion
Finite Time Blow-up
Mild Solution
Navier-Stokes
Coupled System
2018
Suitable Weak Solutions
Liouville Type Theorem
Vorticity
Navier-Stokes Equations
Energy Inequality

Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier–Stokes equations

Farwig, R., Kozono, H. & Wegmann, D., 2018 Jan 1, (Accepted/In press) In : Mathematische Annalen.

Research output: Contribution to journalArticle

Stokes Operator
Maximal Regularity
Exterior Domain
Moving Boundary
Navier-Stokes Equations
4 Citations (Scopus)
Lorentz Spaces
Self-similar Solutions
Navier-Stokes Equations
Mild Solution
Scaling
3 Citations (Scopus)

Navier-Stokes equations with external forces in time-weighted Besov spaces

Kozono, H. & Shimizu, S., 2018 Jan 1, (Accepted/In press) In : Mathematische Nachrichten.

Research output: Contribution to journalArticle

Besov Spaces
Weighted Spaces
Navier-Stokes Equations
Lp Estimates
Implicit Function Theorem
2 Citations (Scopus)

Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces

Kozono, H. & Shimizu, S., 2018 Jan 1, (Accepted/In press) In : Journal of Functional Analysis.

Research output: Contribution to journalArticle

Besov Spaces
Strong Solution
Navier-Stokes Equations
Regularity
Homogeneous Space
2017
9 Citations (Scopus)

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

Kozono, H., Terasawa, Y. & Wakasugi, Y., 2017 Jan 15, In : Journal of Functional Analysis. 272, 2, p. 804-818 15 p.

Research output: Contribution to journalArticle

Dirichlet Integral
Liouville Type Theorem
Navier-Stokes Equations
Scaling
Liouville's theorem
1 Citation (Scopus)

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

Hashimoto, I. & Kozono, H., 2017 May 15, In : Journal of Differential Equations. 262, 10, p. 5133-5159 27 p.

Research output: Contribution to journalArticle

Radially Symmetric Solutions
Fluid Model
Higher Dimensions
Exterior Domain
Asymptotic Behavior

Decay of non-stationary navier-stokes flow with nonzero dirichlet boundary data

Farwig, R., Kozono, H. & Wegmann, D., 2017 Jan 1, In : Indiana University Mathematics Journal. 66, 6, p. 2169-2185 17 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Dirichlet
Decay
Existence of Weak Solutions
1 Citation (Scopus)

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

Farwig, R., Kozono, H. & Wegmann, D., 2017 Sep 1, In : Journal of Mathematical Analysis and Applications. 453, 1, p. 271-286 16 p.

Research output: Contribution to journalArticle

Strong Solution
Navier-Stokes
Dirichlet
Weak Solution
Decay
2016
35 Citations (Scopus)

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

Kozono, H., Miura, M. & Sugiyama, Y., 2016 Mar 1, In : Journal of Functional Analysis. 270, 5, p. 1663-1683 21 p.

Research output: Contribution to journalArticle

Existence and Uniqueness Theorem
Mild Solution
Navier-Stokes
Coupled System
Fluid

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

Jimbo, S., Kozono, H., Teramoto, Y. & Ushikoshi, E., 2016 Apr 16, (Accepted/In press) In : Mathematische Annalen. p. 1-8 8 p.

Research output: Contribution to journalArticle

Stokes Equations
Eigenvalue
First Variation
Vanish
Torus
2014
6 Citations (Scopus)

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

Kozono, H., Mashiko, Y. & Takada, R., 2014 Mar 28, (Accepted/In press) In : Journal of Evolution Equations.

Research output: Contribution to journalArticle

Coriolis Force
Time-periodic Solutions
Asymptotic Stability
Periodic Solution
Navier-Stokes Equations
1 Citation (Scopus)

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

Kanbayashi, N., Kozono, H. & Okabe, T., 2014 Jan 1, In : Journal of Mathematical Analysis and Applications. 409, 1, p. 378-392 15 p.

Research output: Contribution to journalArticle

Stationary Solutions
Navier Stokes equations
Navier-Stokes Equations
Boundary conditions
Fluxes
7 Citations (Scopus)
Energy Inequality
Exterior Domain
Boundary Value
Navier Stokes equations
Weak Solution
2013

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

Kozono, H. & Yanagisawa, T., 2013 Jul, In : Manuscripta Mathematica. 141, 3-4, p. 637-662 26 p.

Research output: Contribution to journalArticle

Elliptic Systems
Boundary Value Problem
Banach space
Null Space
Fluid Mechanics
3 Citations (Scopus)

Global Compensated Compactness Theorem for General Differential Operators of First Order

Kozono, H. & Yanagisawa, T., 2013, In : Archive for Rational Mechanics and Analysis. 207, 3, p. 879-905 27 p.

Research output: Contribution to journalArticle

Compensated Compactness
Differential operator
First-order
Adjoint Operator
Manifolds with Boundary
6 Citations (Scopus)

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

Kozono, H. & Ushikoshi, E., 2013, In : Archive for Rational Mechanics and Analysis. 208, 3, p. 1005-1055 51 p.

Research output: Contribution to journalArticle

Green's Matrix
Representation Formula
Boundary Integral
Stokes Equations
Elliptic Boundary Value Problems
11 Citations (Scopus)

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

Heck, H., Kim, H. & Kozono, H., 2013 Jun, In : Mathematische Annalen. 356, 2, p. 653-681 29 p.

Research output: Contribution to journalArticle

Stationary Navier-Stokes Equations
Viscous Fluid
Incompressible Fluid
Weak Solution
Equality
2012
6 Citations (Scopus)

Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space

Kozono, H., Sugiyama, Y. & Wachi, T., 2012 Jan 15, In : Journal of Differential Equations. 252, 2, p. 1213-1228 16 p.

Research output: Contribution to journalArticle

Existence and Uniqueness Theorem
Mild Solution
Scaling
Invariant
Existence and Uniqueness of Solutions
5 Citations (Scopus)

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

Kozono, H., Sugiyama, Y. & Yahagi, Y., 2012 Oct 1, In : Journal of Differential Equations. 253, 7, p. 2295-2313 19 p.

Research output: Contribution to journalArticle

Existence and Uniqueness Theorem
Weak Solution
Local Existence
Existence Theorem
Uniqueness
6 Citations (Scopus)

Leray's inequality in general multi-connected domains in ℝ n

Farwig, R., Kozono, H. & Yanagisawa, T., 2012 Sep, In : Mathematische Annalen. 354, 1, p. 137-145 9 p.

Research output: Contribution to journalArticle

Stationary Navier-Stokes Equations
Hypersurface
Existence of Solutions
Bounded Domain
If and only if
6 Citations (Scopus)

On the stationary Navier-Stokes equations in exterior domains

Kim, H. & Kozono, H., 2012 Nov 15, In : Journal of Mathematical Analysis and Applications. 395, 2, p. 486-495 10 p.

Research output: Contribution to journalArticle

Stationary Navier-Stokes Equations
Exterior Domain
Navier Stokes equations
Weak Solution
Energy Inequality
8 Citations (Scopus)

On the stationary Navier-Stokes flows around a rotating body

Heck, H., Kim, H. & Kozono, H., 2012 Jul, In : Manuscripta Mathematica. 138, 3-4, p. 315-345 31 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Rotating
Stationary Navier-Stokes Equations
Incompressible Navier-Stokes
2011
5 Citations (Scopus)
Global Weak Solutions
Navier-Stokes System
Divergence
Navier-Stokes Equations
Weak Solution

Preface

Yukie, A., Bando, S., Hanamura, M., Kozono, H., Miyaoka, R., Takagi, I., Takeda, M., Tanaka, K., Tsuzuki, N., Ishida, M., Nishikawa, S. & Oda, T., 2011 Dec, In : Tohoku Mathematical Journal. 63, 4

Research output: Contribution to journalArticle

2010
4 Citations (Scopus)

Global weak solutions of the Navier-Stokes system with nonzero boundary conditions

Farwig, R., Kozono, H. & Sohr, H., 2010 Aug, In : Funkcialaj Ekvacioj. 53, 2, p. 231-247 17 p.

Research output: Contribution to journalArticle

Global Weak Solutions
Navier-Stokes System
Boundary conditions
Weak Solution
Boundary Value
5 Citations (Scopus)

Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class

Kozono, H., Sugiyama, Y. & Takada, R., 2010 May 1, In : Journal of Mathematical Analysis and Applications. 365, 1, p. 60-66 7 p.

Research output: Contribution to journalArticle

Self-similar Solutions
Nonexistence
Scaling
Invariant
Semilinear
12 Citations (Scopus)

Strong solutions to the Keller-Segel system with the weak L n 2 initial data and its application to the blow-up rate

Kozono, H. & Sugiyama, Y., 2010 May, In : Mathematische Nachrichten. 283, 5, p. 732-751 20 p.

Research output: Contribution to journalArticle

Blow-up Rate
Strong Solution
Local Existence
Self-similar Solutions
Existence of Solutions
2009
12 Citations (Scopus)

Energy-based regularity criteria for the Navier-Stokes equations

Farwig, R., Kozono, H. & Sohr, H., 2009 Oct, In : Journal of Mathematical Fluid Mechanics. 11, 3, p. 428-442 15 p.

Research output: Contribution to journalArticle

Regularity Criterion
regularity
Navier-Stokes equation
Navier Stokes equations
Weak Solution
6 Citations (Scopus)

Global Div-Curl lemma on bounded domains in R3

Kozono, H. & Yanagisawa, T., 2009 Jun 1, In : Journal of Functional Analysis. 256, 11, p. 3847-3859 13 p.

Research output: Contribution to journalArticle

Curl
Lemma
Bounded Domain
Unit normal vector
Hermann Von Helmholtz
25 Citations (Scopus)
Scale Invariant
Strong Solution
Semilinear
Byproducts
Heat Semigroup
27 Citations (Scopus)

Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data

Kozono, H. & Yanagisawa, T., 2009, In : Mathematische Zeitschrift. 262, 1, p. 27-39 13 p.

Research output: Contribution to journalArticle

Stationary Navier-Stokes Equations
Hermann Von Helmholtz
Connected Components
Solvability
Existence of Solutions
39 Citations (Scopus)

Lr-variational inequality for vector fields and the helmholtz-weyl decomposition in bounded domains

Kozono, H. & Yanagisawa, T., 2009, In : Indiana University Mathematics Journal. 58, 4, p. 1853-1920 68 p.

Research output: Contribution to journalArticle

Hermann Von Helmholtz
Variational Inequalities
Bounded Domain
Vector Field
Hodge Decomposition
3 Citations (Scopus)

Nonhomogeneous boundary value problems for stationary navier-stokes equations in a multiply connected bounded domain

Kozono, H. & Yanagisawa, T., 2009 Nov, In : Pacific Journal of Mathematics. 243, 1, p. 127-150 24 p.

Research output: Contribution to journalArticle

Stationary Navier-Stokes Equations
Multiply Connected Domain
Nonhomogeneous Boundary Conditions
Existence of Weak Solutions
Hermann Von Helmholtz
21 Citations (Scopus)

On the Stokes operator in general unbounded domains

Farwig, R., Kozono, H. & Sohr, H., 2009 Jan 1, In : Hokkaido Mathematical Journal. 38, 1, p. 111-136 26 p.

Research output: Contribution to journalArticle

Stokes Operator
Maximal Regularity
Unbounded Domain
Well-defined
Resolvent Estimates
6 Citations (Scopus)

Stability of plane Couette flows with respect to small periodic perturbations

Heck, H., Kim, H. & Kozono, H., 2009 Nov 1, In : Nonlinear Analysis, Theory, Methods and Applications. 71, 9, p. 3739-3758 20 p.

Research output: Contribution to journalArticle

Couette Flow
Exponential Stability
Asymptotic stability
Perturbation
Norm
2008
29 Citations (Scopus)

Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system

Kozono, H. & Sugiyama, Y., 2008 May, In : Journal of Evolution Equations. 8, 2, p. 353-378 26 p.

Research output: Contribution to journalArticle

Finite Time Blow-up
Blow-up of Solutions
Local Existence
Mild Solution
Blow-up Rate
30 Citations (Scopus)

Remarks on Gagliardo-Nirenberg type inequality with critical Sobolev space and BMO

Kozono, H. & Wadade, H., 2008 Aug, In : Mathematische Zeitschrift. 259, 4, p. 935-950 16 p.

Research output: Contribution to journalArticle

Sobolev Spaces
Gagliardo-Nirenberg Inequalities
Norm
Optimal Growth
End point
27 Citations (Scopus)
Self-similar Solutions
Strong Solution
Heat Semigroup
Smoothing Effect
Fractional Powers
2007
17 Citations (Scopus)

Local in time regularity properties of the Navier-Stokes equations

Farwig, R., Kozono, H. & Sohr, H., 2007, In : Indiana University Mathematics Journal. 56, 5, p. 2111-2131 21 p.

Research output: Contribution to journalArticle

Global Regularity
Regularity Properties
Navier-Stokes Equations
Regularity Conditions
Weak Solution
33 Citations (Scopus)

On the Helmholtz decomposition in general unbounded domains

Farwig, R., Kozono, H. & Sohr, H., 2007 Mar, In : Archiv der Mathematik. 88, 3, p. 239-248 10 p.

Research output: Contribution to journalArticle

Helmholtz Decomposition
Unbounded Domain
Stokes Operator
Hermann Von Helmholtz
n-dimensional
30 Citations (Scopus)

Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data

Farwig, R., Kozono, H. & Sohr, H., 2007 Jan, In : Journal of the Mathematical Society of Japan. 59, 1, p. 127-150 24 p.

Research output: Contribution to journalArticle

Very Weak Solutions
Exterior Domain
Navier-Stokes Equations
Trace Theorem
Differentiability
2006
18 Citations (Scopus)

A removable isolated singularity theorem for the stationary Navier-Stokes equations

Kim, H. & Kozono, H., 2006 Jan 1, In : Journal of Differential Equations. 220, 1, p. 68-84 17 p.

Research output: Contribution to journalArticle

Removable Singularity
Stationary Navier-Stokes Equations
Isolated Singularity
Smooth Solution
Navier Stokes equations
38 Citations (Scopus)

Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality

Kozono, H., Sato, T. & Wadade, H., 2006, In : Indiana University Mathematics Journal. 55, 6, p. 1951-1974 24 p.

Research output: Contribution to journalArticle

Trudinger-Moser Inequality
Gagliardo-Nirenberg Inequalities
Best Constants
Upper bound
Hubert Space
2005
81 Citations (Scopus)

An Lq-approach to Stokes and Navier-Stokes equations in general domains

Farwig, R., Kozono, H. & Sohr, H., 2005, In : Acta Mathematica. 195, 1, p. 21-53 33 p.

Research output: Contribution to journalArticle

Stokes
Navier-Stokes Equations
2004
52 Citations (Scopus)

Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations

Kozono, H. & Shimada, Y., 2004, In : Mathematische Nachrichten. 276, p. 63-74 12 p.

Research output: Contribution to journalArticle

Bilinear Estimates
Triebel-Lizorkin Space
Continuation Theorem
Strong Solution
Homogeneous Space
29 Citations (Scopus)

Extension criterion via two-components of vorticity on strong solutions to the 3 D Navier-Stokes equations

Kozono, H. & Yatsu, N., 2004 Jan, In : Mathematische Zeitschrift. 246, 1-2, p. 55-68 14 p.

Research output: Contribution to journalArticle

Strong Solution
Vorticity
3D
Navier-Stokes Equations
Regularity Criterion
24 Citations (Scopus)

Interior regularity criteria in weak spaces for the Navier-Stokes equations

Kim, H. & Kozono, H., 2004 Sep, In : Manuscripta Mathematica. 115, 1, p. 85-100 16 p.

Research output: Contribution to journalArticle

Regularity Criterion
Weak Solution
Navier-Stokes Equations
Interior
Incompressible Navier-Stokes Equations