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

• 2023

  Removable time-dependent singularities of solutions to the Stokes equations

  Kozono, H., Ushikoshi, E. & Wakabayashi, F., 2023 1月 5, In: Journal of Differential Equations. 342, p. 472-489 18 p.

  研究成果: Article › 査読

  • Stokes Equation 100%
  • Classical Solution 50%

• Stability of stationary solutions to the Navier–Stokes equations in the Besov space

  Kozono, H. & Shimizu, S., 2023 5月, In: Mathematische Nachrichten. 296, 5, p. 1964-1982 19 p.

  研究成果: Article › 査読

  • Stationary Solution 100%
  • Stability 100%
  • Besov Space 50%
  • unique solution φ 50%
  • Solution Formula 50%
• 2022

  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%
  • Bounded Domain 50%
  • Vector Field 25%
  • Boundary Condition 25%
  • Betti Number 25%
  1 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

  • Navier-Stokes Equation 100%
  • Stationary Problem 100%
  • Liouville Type 100%
  • Classes 100%
  • Exterior Domain 50%
  1 被引用数 (Scopus)

• 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

  • Navier-Stokes Equation 100%
  • Asymptotic Property 50%
  • Liouville Type 50%
  • Asymptotic Behavior 50%
• 2021

  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

  • Elliptic Equation 100%
  • Liouville Type 50%
  • Order 50%
  • Asymptotic Behavior 50%
  • Parabolic Equation 50%

• 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

  • Vector Field 100%
  • Exterior Domain 100%
  • Variational Inequality 50%
  • Elliptic Boundary Value Problem 50%
  • Weak Solution 50%
  3 被引用数 (Scopus)

• Necessary and sufficient condition on initial data in the Besov space for solutions in the Serrin class of the Navier–Stokes equations

  Kozono, H., Okada, A. & Shimizu, S., 2021 9月, In: Journal of Evolution Equations. 21, 3, p. 3015-3033 19 p.

  研究成果: Article › 査読

  • Initial Datum 100%
  • Besov Space 60%
  • Necessary and Sufficient Condition 40%
  • Classes 40%
  • Lorentz Space 20%

• Stationary Navier–Stokes equations under inhomogeneous boundary conditions in 3D exterior domains

  Hieber, M., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2021 10月, In: Calculus of Variations and Partial Differential Equations. 60, 5, 180.

  研究成果: Article › 査読

  • Exterior Domain 100%
  • Satisfying 100%
  • Weak Solution 100%
  • Boundary Condition 50%
  • Closed Surface 50%
  1 被引用数 (Scopus)

• The Helmholtz–Weyl decomposition of L^r vector fields for two dimensional exterior domains

  Hieber, M., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2021 5月, In: Journal of Geometric Analysis. 31, 5, p. 5146-5165 20 p.

  研究成果: Article › 査読

  • Exterior Domain 100%
  • Harmonic Vector Field 100%
  • Vector Field 50%
  • Boundary Condition 50%
  • Modulo 50%
  4 被引用数 (Scopus)

• The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary

  Farwig, R., Kozono, H., Tsuda, K. & Wegmann, D., 2021 10月, In: Nonlinear Analysis: Real World Applications. 61, 103339.

  研究成果: Article › 査読

  • Bounded Domain 100%
  • Periodic Problem 100%
  • Parabolic 50%
  • Problem Domain 50%
  • Periodic Solution 50%
  6 被引用数 (Scopus)
• 2020

  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%
  • Vector Field 50%
  • Boundary Condition 50%
  • Harmonic Vector Field 50%
  • Simple Closed Curve 50%
  4 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

  • Initial Datum 100%
  • Classes 75%
  • Navier-Stokes Equation 50%
  • Homogeneous Besov Space 50%
  • Priori Estimate 25%
  9 被引用数 (Scopus)
• 2019

  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

  • Operators 100%
  • Exterior Domain 75%
  • Dirichlet Boundary Condition 25%
  • time interval τ 25%
  • Existence Theorem 25%
  4 被引用数 (Scopus)

• Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

  Kaneko, K., Kozono, H. & Shimizu, S., 2019, In: Indiana University Mathematics Journal. 68, 3, p. 857-880 24 p.

  研究成果: Article › 査読

  • Navier-Stokes Equation 100%
  • Homogeneous Besov Space 100%
  • Stationary Problem 50%
  • Stationary Solution 50%
  • Besov Space 50%
  11 被引用数 (Scopus)

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

  Kozono, H. & Shimizu, S., 2019 2月 1, In: Journal of Functional Analysis. 276, 3, p. 896-931 36 p.

  研究成果: Article › 査読

  Open Access

  • Strong Solution 100%
  • Initial Datum 100%
  • Homogeneous Besov Space 100%
  • Regularity Theorem 100%
  • Force 100%
  17 被引用数 (Scopus)

• Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with the Navier-Stokes fluid

  Kozono, H., Miura, M. & Sugiyama, Y., 2019 10月 15, In: Journal of Differential Equations. 267, 9, p. 5410-5492 83 p.

  研究成果: Article › 査読

  • Mild Solution 100%
  • Initial Datum 66%
  • Finite Time 33%
  • Global Existence 33%
  • Fluid Motion 33%
  7 被引用数 (Scopus)
• 2018

  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

  • Weak Solution 100%
  • Classes 66%
  • Growth Condition 33%
  • Unbounded Domain 33%
  • Liouville Type 33%
  1 被引用数 (Scopus)

• Navier–Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions

  Kozono, H. & Shimizu, S., 2018 2月 15, In: Journal of Mathematical Analysis and Applications. 458, 2, p. 1693-1708 16 p.

  研究成果: Article › 査読

  • Initial Datum 100%
  • Lorentz Space 100%
  • Force 100%
  • Mild Solution 66%
  • Stokes Equation 33%
  7 被引用数 (Scopus)

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

  Kozono, H. & Shimizu, S., 2018 8月, In: Mathematische Nachrichten. 291, 11-12, p. 1781-1800 20 p.

  研究成果: Article › 査読

  • Besov Space 100%
  • Datum 66%
  • Time 66%
  • External Force 66%
  • Mild Solution 33%
  11 被引用数 (Scopus)
• 2017

  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

  • Priori Estimate 100%
  • Space Dimension 100%
  • Liouville Type 100%
  • Liouville's Theorem 100%
  • Scaling Property 100%
  48 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

  • Exterior Domain 100%
  • Asymptotics 50%
  • Space Dimension 50%
  • Asymptotic Stability 50%
  • Damped Wave Equation 50%
  1 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

  • Weak Solution 100%
  • Navier-Stokes Equation 50%
  • Exterior Domain 50%
  • Upper Bound 50%
  • Satisfying 50%

• 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

  • Weak Solution 100%
  • Boundary Value 50%
  • Strong Solution 50%
  • Approximate Solution 50%
  • Satisfying 50%
  2 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 Equation 100%
  • Geometry 33%
  • 2-Dimensional Torus 33%
  • Variations 33%
  1 被引用数 (Scopus)
• 2016

  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

  • Initial Datum 100%
  • Mild Solution 50%
  • Existence 50%
  • Invariant Space 25%
  • Asymptotic Stability 25%
  91 被引用数 (Scopus)
• 2014

  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

  • Periodic Solution 100%
  • Navier-Stokes Equation 66%
  • Asymptotic Stability 66%
  • Coriolis Force 33%
  • Periodic Problem 33%
  10 被引用数 (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 1月 1, In: Journal of Mathematical Analysis and Applications. 409, 1, p. 378-392 15 p.

  研究成果: Article › 査読

  • Navier-Stokes Equation 100%
  • Stability 100%
  • Bounded Domain 50%
  • Stationary Solution 50%
  • Nonhomogeneous Boundary Condition 50%
  1 被引用数 (Scopus)

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

  Farwig, R. & Kozono, H., 2014 4月 1, In: Journal of Differential Equations. 256, 7, p. 2633-2658 26 p.

  研究成果: Article › 査読

  • Weak Solution 100%
  • Boundary Value 75%
  • Satisfying 75%
  • Navier-Stokes Equation 50%
  • Exterior Domain 50%
  8 被引用数 (Scopus)
• 2013

  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

  • Banach Space 100%
  • Boundary Value Problems 66%
  • Milgram Theorem 66%
  • Hilbert Spaces 33%
  • Variational Inequality 33%
  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

  • Differential Operator 100%
  • Order 66%
  • Bounded Domain 33%
  • Compact Riemannian Manifold 33%
  • Integral Formula 33%
  5 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

  • Stokes Equation 100%
  • Green Function 100%
  • Matrix 50%
  • Boundary Value Problems 50%
  • Bounded Domain 50%
  7 被引用数 (Scopus)

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

  Heck, H., Kim, H. & Kozono, H., 2013 6月, In: Mathematische Annalen. 356, 2, p. 653-681 29 p.

  研究成果: Article › 査読

  • Weak Solution 100%
  • Navier-Stokes Equation 25%
  • Equality 25%
  • Priori Estimate 12%
  • Exterior Domain 12%
  15 被引用数 (Scopus)
• 2012

  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

  Open Access

  • Mild Solution 100%
  • Parabolic 100%
  • Invariant Space 100%
  • Initial Datum 100%
  • Parabolic Type 100%
  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

  Open Access

  • Weak Solution 100%
  • Parabolic 50%
  • Existence Theorem 25%
  • Initial Datum 25%
  • Elliptic Type 25%
  19 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

  • Sphere 100%
  • Navier-Stokes Equation 50%
  • Hypersurfaces 50%
  • Bounded Domain 50%
  • Zeros 50%
  8 被引用数 (Scopus)

• On the stationary Navier-Stokes equations in exterior domains

  Kim, H. & Kozono, H., 2012 11月 15, In: Journal of Mathematical Analysis and Applications. 395, 2, p. 486-495 10 p.

  研究成果: Article › 査読

  • Weak Solution 100%
  • Navier-Stokes Equation 40%
  • Exterior Domain 40%
  • Satisfying 40%
  • Smallness 20%
  8 被引用数 (Scopus)

• On the stationary Navier-Stokes flows around a rotating body

  Heck, H., Kim, H. & Kozono, H., 2012 7月, In: manuscripta mathematica. 138, 3-4, p. 315-345 31 p.

  研究成果: Article › 査読

  • Rotation 100%
  • Satisfying 66%
  • Navier-Stokes Equation 33%
  • Exponents 33%
  • Angular Velocity 33%
  10 被引用数 (Scopus)
• 2011

  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

  • Weak Solution 100%
  • Satisfying 75%
  • Classes 50%
  • General System 50%
  • Vector Field 25%
  8 被引用数 (Scopus)
• 2010

  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

  • Weak Solution 100%
  • Boundary Value 40%
  • Boundary Condition 20%
  • Navier-Stokes Equation 20%
  • Initial Value 20%
  5 被引用数 (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 5月 1, In: Journal of Mathematical Analysis and Applications. 365, 1, p. 60-66 7 p.

  研究成果: Article › 査読

  • Finite Time 100%
  • Classes 100%
  • Nonexistence 66%
  • Parabolic 66%
  • Semilinear 33%
  5 被引用数 (Scopus)

• Strong solutions to the Keller-Segel system with the weak L ⁿ₂ initial data and its application to the blow-up rate

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

  研究成果: Article › 査読

  • Strong Solution 100%
  • Initial Datum 100%
  • time interval τ 50%
  • Solution Exists 50%
  • Give Solution 50%
  19 被引用数 (Scopus)
• 2009

  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

  • Weak Solution 100%
  • Navier-Stokes Equation 33%
  • Energy Dissipation 33%
  • time interval τ 33%
  • Inf 33%
  11 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

  Open Access

  • Bounded Domain 100%
  • Vector Field 50%
  • Open Set 50%
  • Converges 50%
  10 被引用数 (Scopus)

• 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

  Open Access

  • Strong Solution 100%
  • Parabolic 100%
  • Parabolic Type 100%
  • Invariant Space 50%
  • Initial Datum 50%
  37 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

  • Navier-Stokes Equation 100%
  • Total Sum 50%
  • Solvability 50%
  • Connected Component 50%
  • Bounded Domain 50%
  31 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

  • Vector Field 100%
  • Bounded Domain 66%
  • Boundary Condition 33%
  • Vector Potential 33%
  • Vector Space 33%
  64 被引用数 (Scopus)

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

  Kozono, H. & Yanagisawa, T., 2009 11月, In: Pacific Journal of Mathematics. 243, 1, p. 127-150 24 p.

  研究成果: Article › 査読

  • Navier-Stokes Equation 100%
  • Bounded Domain 100%
  • Vector Field 50%
  • Boundary Condition 50%
  • Sufficient Condition 50%
  6 被引用数 (Scopus)

• On the Stokes operator in general unbounded domains

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

  研究成果: Article › 査読

  Open Access

  • Operators 100%
  • Smooth Domain 66%
  • Unbounded Domain 66%
  • Dimensional Case 33%
  • Resolvent 33%
  27 被引用数 (Scopus)

• Stability of plane Couette flows with respect to small periodic perturbations

  Heck, H., Kim, H. & Kozono, H., 2009 11月 1, In: Nonlinear Analysis, Theory, Methods and Applications. 71, 9, p. 3739-3758 20 p.

  研究成果: Article › 査読

  • Flow 100%
  • Stability 100%
  • Integer 50%
  7 被引用数 (Scopus)