小薗 英雄

研究成果

年別の研究成果 1985 1998 2009 2010 2012 2013 2017 2018 2019 2021 2023

• 99 Article
• 4 Editorial
• 3 Chapter
• 1 Conference contribution

年別の研究成果

年別の研究成果

検索結果

• Article

  A Characterization of Harmonic L^r -Vector Fields in Three Dimensional Exterior Domains

  Hieber, M., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2022 7月, In: Journal of Geometric Analysis. 32, 7, 206.

  研究成果: Article › 査読

  • Exterior Domain 100%
  • Harmonic 74%
  • Vector Field 71%
  • Three-dimensional 62%
  • Characterization 46%
  1 被引用数 (Scopus)

• A Characterization of Harmonic L^r -Vector Fields in Two-Dimensional Exterior Domains

  Hieber, M., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2020 12月 1, In: Journal of Geometric Analysis. 30, 4, p. 3742-3759 18 p.

  研究成果: Article › 査読

  • Exterior Domain 100%
  • Harmonic 74%
  • Vector Field 71%
  • Characterization 46%
  • Unit normal vector 28%
  4 被引用数 (Scopus)

• An L^q-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.

  研究成果: Article › 査読
  106 被引用数 (Scopus)

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

  Kozono, H., Terasawa, Y. & Wakasugi, Y., 2017 1月 15, In: Journal of Functional Analysis. 272, 2, p. 804-818 15 p.

  研究成果: Article › 査読

  • Dirichlet Integral 100%
  • Liouville Type Theorem 94%
  • Scaling 63%
  • Navier-Stokes Equations 60%
  • Liouville's theorem 47%
  48 被引用数 (Scopus)

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

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

  研究成果: Article › 査読

  • Removable Singularity 100%
  • Stationary Navier-Stokes Equations 97%
  • Isolated Singularity 84%
  • Byproducts 74%
  • Smooth Solution 72%
  28 被引用数 (Scopus)

• A stable manifold theorem for the Yang-Mills gradient flow

  Naito, H., Kozono, H. & Maeda, Y., 1990 3月, In: Tohoku Mathematical Journal. 42, 1, p. 45-66 22 p.

  研究成果: Article › 査読

  Open Access
  2 被引用数 (Scopus)

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

  Hashimoto, I. & Kozono, H., 2017 5月 15, In: Journal of Differential Equations. 262, 10, p. 5133-5159 27 p.

  研究成果: Article › 査読

  • Radially Symmetric Solutions 100%
  • Fluid Model 92%
  • Higher Dimensions 69%
  • Exterior Domain 57%
  • Asymptotic Behavior 53%
  1 被引用数 (Scopus)

• Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains

  Kozono, H., Terasawa, Y. & Wakasugi, Y., 2021 8月, In: Mathematische Annalen. 380, 3-4, p. 1105-1117 13 p.

  研究成果: Article › 査読

  • Unbounded Coefficients 100%
  • Liouville Type Theorem 94%
  • Asymptotic Behavior of Solutions 76%
  • Unbounded Domain 75%
  • Elliptic Equations 66%

• Asymptotic behaviour in L ^r for weak solutions of the Navier-Stokes equations in exterior domains

  Kozono, H., Ogawa, T. & Sohr, H., 1992 12月 1, In: Manuscripta Mathematica. 74, 1, p. 253-275 23 p.

  研究成果: Article › 査読
  16 被引用数 (Scopus)

• Asymptotic Properties of Steady and Nonsteady Solutions to the 2D Navier-Stokes Equations with Finite Generalized Dirichlet Integral

  Kozono, H., Terasawa, Y. & Wakasugi, Y., 2022, In: Indiana University Mathematics Journal. 71, 5, p. 1299-1316 18 p.

  研究成果: Article › 査読

  • Dirichlet Integral 100%
  • Liouville Type Theorem 94%
  • Navier-Stokes Equations 60%
  • Exterior Domain 41%
  • Asymptotic Behavior of Solutions 38%

• Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl

  Kozono, H., Terasawa, Y. & Wakasugi, Y., 2022 1月 15, In: Journal of Functional Analysis. 282, 2, 109289.

  研究成果: Article › 査読

  • Dirichlet Integral 100%
  • Liouville Type Theorem 94%
  • Decay Estimates 82%
  • Vorticity 75%
  • Navier-Stokes Equations 60%

• Asymptotic Stability of Large Solutions with Large Perturbation to the Navier-Stokes Equations

  Kozono, H., 2000 10月 1, In: Journal of Functional Analysis. 176, 2, p. 153-197 45 p.

  研究成果: Article › 査読

  • Energy Inequality 100%
  • Large Solutions 99%
  • Unbounded Domain 77%
  • Disturbance 72%
  • Asymptotic Stability 69%
  22 被引用数 (Scopus)

• A Yang-Mills-Higgs gradient flow on R³ blowing up at infinity

  Kozono, H., Maeda, Y. & Naito, H., 1998, In: Proceedings of the Japan Academy Series A: Mathematical Sciences. 74, 5, p. 71-73 3 p.

  研究成果: Article › 査読

  Open Access
  1 被引用数 (Scopus)

• Bilinear estimates in BMO and the Navier-Stokes equations

  Kozono, H. & Taniuchi, Y., 2000 9月, In: Mathematische Zeitschrift. 235, 1, p. 173-194 22 p.

  研究成果: Article › 査読

  • Bilinear Estimates 100%
  • Vorticity 70%
  • Smooth Solution 69%
  • Blow-up 60%
  • Weak Solution 56%
  195 被引用数 (Scopus)

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

  Kozono, H. & Shimada, Y., 2004 1月 1, In: Mathematische Nachrichten. 276, p. 63-74 12 p.

  研究成果: Article › 査読

  • Bilinear Estimates 100%
  • Triebel-Lizorkin Space 85%
  • Continuation Theorem 84%
  • Homogeneous Space 69%
  • Strong Solution 67%
  68 被引用数 (Scopus)

• Characterization of initial data in the homogeneous Besov space for solutions in the Serrin class of the Navier-Stokes equations

  Kozono, H., Okada, A. & Shimizu, S., 2020 3月 15, In: Journal of Functional Analysis. 278, 5, 108390.

  研究成果: Article › 査読

  • Besov Spaces 100%
  • Homogeneous Space 97%
  • Navier-Stokes Equations 79%
  • Characterization 50%
  • Stokes Flow 36%
  9 被引用数 (Scopus)

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

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

  研究成果: Article › 査読

  • Stokes Flow 100%
  • Navier-Stokes 90%
  • Dirichlet 76%
  • Decay 71%
  • Exterior Domain 48%

• Decay properties of strong solutions for the navier-stokes equations in two-dimensional unbounded domains

  Kozono, H. & Ogawa, T., 1993 5月 1, In: Archive for Rational Mechanics and Analysis. 122, 1, p. 1-17 17 p.

  研究成果: Article › 査読
  9 被引用数 (Scopus)

• Density properties for solenoidal vector fields, with applications to the Navier-Stokes equations in exterior domains

  Kozono, H. & Sohr, H., 1992 4月, In: Journal of the Mathematical Society of Japan. 44, 2, p. 307-330 24 p.

  研究成果: Article › 査読
  10 被引用数 (Scopus)

• Energy-based regularity criteria for the Navier-Stokes equations

  Farwig, R., Kozono, H. & Sohr, H., 2009 10月, In: Journal of Mathematical Fluid Mechanics. 11, 3, p. 428-442 15 p.

  研究成果: Article › 査読

  • Regularity Criterion 100%
  • Kinetic energy 86%
  • regularity 84%
  • Navier Stokes equations 80%
  • Navier-Stokes equation 79%
  11 被引用数 (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 3月 1, In: Journal of Functional Analysis. 270, 5, p. 1663-1683 21 p.

  研究成果: Article › 査読

  • Existence and Uniqueness Theorem 100%
  • Navier-Stokes 93%
  • Mild Solution 93%
  • Coupled System 86%
  • Fluid 69%
  91 被引用数 (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 1月 15, In: Journal of Differential Equations. 252, 2, p. 1213-1228 16 p.

  研究成果: Article › 査読

  • Existence and Uniqueness Theorem 100%
  • Mild Solution 93%
  • Scaling 76%
  • Invariant 49%
  • Existence and Uniqueness of Solutions 43%
  10 被引用数 (Scopus)

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

  Kozono, H., Sugiyama, Y. & Yahagi, Y., 2012 10月 1, In: Journal of Differential Equations. 253, 7, p. 2295-2313 19 p.

  研究成果: Article › 査読

  • Existence and Uniqueness Theorem 100%
  • Weak Solution 73%
  • Local Existence 32%
  • Existence Theorem 26%
  • Scaling 25%
  19 被引用数 (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 9月, In: Journal of Evolution Equations. 14, 3, p. 565-601 37 p.

  研究成果: Article › 査読

  • Coriolis Force 100%
  • Time-periodic Solutions 89%
  • Asymptotic Stability 62%
  • Navier-Stokes Equations 56%
  • Periodic Solution 54%
  10 被引用数 (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 9月 1, In: Journal of Mathematical Analysis and Applications. 453, 1, p. 271-286 16 p.

  研究成果: Article › 査読

  Open Access

  • Navier-Stokes 100%
  • Strong Solution 94%
  • Dirichlet 84%
  • Weak Solution 78%
  • Decay 78%
  2 被引用数 (Scopus)

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

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

  研究成果: Article › 査読

  • 3D 100%
  • Vorticity 95%
  • Strong Solution 92%
  • Navier-Stokes Equations 76%
  • Regularity Criterion 57%
  34 被引用数 (Scopus)

• Exterior problem for the stationary Navier-Stokes equations in the Lorentz space

  Kozono, H. & Yamazaki, M., 1998 2月, In: Mathematische Annalen. 310, 2, p. 279-305 27 p.

  研究成果: Article › 査読
  49 被引用数 (Scopus)

• Finite energy of generalized suitable weak solutions to the Navier–Stokes equations and Liouville-type theorems in two dimensional domains

  Kozono, H., Terasawa, Y. & Wakasugi, Y., 2018 8月 15, In: Journal of Differential Equations. 265, 4, p. 1227-1247 21 p.

  研究成果: Article › 査読

  Open Access

  • Suitable Weak Solutions 100%
  • Liouville Type Theorem 89%
  • Vorticity 80%
  • Navier-Stokes Equations 57%
  • Energy 46%
  1 被引用数 (Scopus)

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

  Kozono, H. & Yanagisawa, T., 2013 7月, In: Manuscripta Mathematica. 141, 3-4, p. 637-662 26 p.

  研究成果: Article › 査読

  • Elliptic Systems 100%
  • Boundary Value Problem 66%
  • Banach space 64%
  • Fluid Mechanics 55%
  • Bilinear form 51%
  12 被引用数 (Scopus)

• Global Compensated Compactness Theorem for General Differential Operators of First Order

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

  研究成果: Article › 査読

  • Compensated Compactness 100%
  • Differential operator 61%
  • First-order 50%
  • Adjoint Operator 48%
  • Manifolds with Boundary 42%
  6 被引用数 (Scopus)

• Global Div-Curl lemma on bounded domains in R³

  Kozono, H. & Yanagisawa, T., 2009 6月 1, In: Journal of Functional Analysis. 256, 11, p. 3847-3859 13 p.

  研究成果: Article › 査読

  • Curl 100%
  • Bounded Domain 67%
  • Unit normal vector 37%
  • Hermann Von Helmholtz 32%
  • Open set 26%
  10 被引用数 (Scopus)

• Global Lⁿ-solution and its decay property for the Navier-Stokes equations in half-space R₊ⁿ

  Kozono, H., 1989 5月, In: Journal of Differential Equations. 79, 1, p. 79-88 10 p.

  研究成果: Article › 査読
  33 被引用数 (Scopus)

• Global solution for the Yang-Mills gradient flow on 4-manifolds

  Kozono, H., Maeda, Y. & Naito, H., 1995 9月, In: Nagoya Mathematical Journal. 139, p. 93-128 36 p.

  研究成果: Article › 査読

  Open Access
  6 被引用数 (Scopus)

• Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries

  Kozono, H. & Ogawa, T., 1994 5月 1, In: Mathematische Zeitschrift. 216, 1, p. 1-30 30 p.

  研究成果: Article › 査読
  9 被引用数 (Scopus)

• Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains

  Kozono, H. & Sohr, H., 1999 9月 10, In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 16, 5, p. 535-561 27 p.

  研究成果: Article › 査読

  Open Access

  • Unbounded Domain 100%
  • Strong Solution 96%
  • Navier Stokes equations 96%
  • Navier-Stokes equation 95%
  • Navier-Stokes Equations 80%

• Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces

  Kozono, H. & Sugiyama, Y., 2009 7月 1, In: Journal of Differential Equations. 247, 1, p. 1-32 32 p.

  研究成果: Article › 査読

  • Scale Invariant 100%
  • Byproducts 84%
  • Strong Solution 80%
  • Semilinear 75%
  • Heat Semigroup 54%
  37 被引用数 (Scopus)

• Global Weak Solutions of the Navier-Stokes Equations with Nonhomogeneous Boundary Data and Divergence

  Farwig, R., Kozono, H. & Sohr, H., 2011, In: Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova. 125, p. 51-70 20 p.

  研究成果: Article › 査読

  Open Access

  • Global Weak Solutions 100%
  • Navier-Stokes System 96%
  • Navier-Stokes equation 81%
  • Divergence 74%
  • divergence 74%
  8 被引用数 (Scopus)

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

  Farwig, R., Kozono, H. & Sohr, H., 2010 8月, In: Funkcialaj Ekvacioj. 53, 2, p. 231-247 17 p.

  研究成果: Article › 査読

  • Global Weak Solutions 100%
  • Navier-Stokes System 96%
  • Boundary conditions 54%
  • Weak Solution 41%
  • Energy Inequality 22%
  5 被引用数 (Scopus)

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

  Jimbo, S., Kozono, H., Teramoto, Y. & Ushikoshi, E., 2017 6月 1, In: Mathematische Annalen. 368, 1-2, p. 877-884 8 p.

  研究成果: Article › 査読

  • Stokes Equations 100%
  • First Variation 59%
  • Eigenvalue 56%
  • Vanish 38%
  • Torus 36%
  1 被引用数 (Scopus)

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

  Kozono, H. & Ushikoshi, E., 2013 6月, In: Archive for Rational Mechanics and Analysis. 208, 3, p. 1005-1055 51 p.

  研究成果: Article › 査読

  • Green's Matrix 100%
  • Green's function 78%
  • Representation Formula 76%
  • Boundary value problems 74%
  • Stokes Equations 74%
  7 被引用数 (Scopus)

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

  Kim, H. & Kozono, H., 2004 9月 1, In: Manuscripta Mathematica. 115, 1, p. 85-100 16 p.

  研究成果: Article › 査読

  • Regularity Criterion 100%
  • Weak Solution 67%
  • Navier-Stokes Equations 67%
  • Interior 66%
  • Incompressible Navier-Stokes Equations 43%
  34 被引用数 (Scopus)

• L¹-solutions of the Navier-Stokes equations in exterior domains

  Kozono, H., 1998 10月, In: Mathematische Annalen. 312, 2, p. 319-340 22 p.

  研究成果: Article › 査読
  30 被引用数 (Scopus)

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

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

  研究成果: Article › 査読

  • Stationary Navier-Stokes Equations 100%
  • Hypersurface 63%
  • Existence of Solutions 58%
  • Bounded Domain 57%
  • Unit 50%
  8 被引用数 (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.

  研究成果: Article › 査読

  • Stationary Navier-Stokes Equations 100%
  • Hermann Von Helmholtz 27%
  • Viscosity 22%
  • Harmonic 20%
  • Solvability 20%
  44 被引用数 (Scopus)

• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations

  Kozono, H. & Taniuchi, Y., 2000 10月, In: Communications in Mathematical Physics. 214, 1, p. 191-200 10 p.

  研究成果: Article › 査読

  • Logarithmic Sobolev Inequality 100%
  • Blow-up Criterion 98%
  • Sobolev Inequality 90%
  • norms 84%
  • Critical Exponents 82%
  158 被引用数 (Scopus)

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

  Kozono, H. & Sugiyama, Y., 2008 5月, In: Journal of Evolution Equations. 8, 2, p. 353-378 26 p.

  研究成果: Article › 査読

  • Finite Time Blow-up 100%
  • Blow-up of Solutions 95%
  • Local Existence 90%
  • Mild Solution 86%
  • Blow-up Rate 51%
  35 被引用数 (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.

  研究成果: Article › 査読

  • Global Regularity 100%
  • Regularity Properties 88%
  • Navier-Stokes Equations 67%
  • Regularity Conditions 39%
  • Weak Solution 33%
  16 被引用数 (Scopus)

• L^r-Helmholtz-Weyl decomposition for three dimensional exterior domains

  Hieber, M., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2021 10月 15, In: Journal of Functional Analysis. 281, 8, 109144.

  研究成果: Article › 査読

  • Hermann Von Helmholtz 100%
  • Exterior Domain 99%
  • Vector Field 71%
  • Three-dimensional 62%
  • Decompose 56%
  3 被引用数 (Scopus)

• L^r-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.

  研究成果: Article › 査読

  • Hermann Von Helmholtz 100%
  • Variational Inequalities 79%
  • Vector Field 71%
  • Bounded Domain 69%
  • Hodge Decomposition 61%
  64 被引用数 (Scopus)

• 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., 2019 12月 1, In: Mathematische Annalen. 375, 3-4, p. 949-972 24 p.

  研究成果: Article › 査読

  • Stokes Operator 100%
  • Maximal Regularity 93%
  • Moving Boundary 87%
  • Exterior Domain 83%
  • Navier-Stokes Equations 60%
  4 被引用数 (Scopus)