{"id":109,"date":"2022-08-12T11:44:38","date_gmt":"2022-08-12T02:44:38","guid":{"rendered":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab-test\/?page_id=109"},"modified":"2025-08-13T08:57:45","modified_gmt":"2025-08-12T23:57:45","slug":"work","status":"publish","type":"page","link":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/research-theme\/work\/","title":{"rendered":"\u7814\u7a76\u696d\u7e3e"},"content":{"rendered":"

Navier-Stokes\u65b9\u7a0b\u5f0f\u95a2\u4fc2<\/h2>\n

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  1. H. Kikuchi, T. Kubo, R. Matsui, Existence of Weak Solution to the Navier-Stokes Equations Approximated by Pressure Stabilization Method,
    \nJournal of Mathematical Fluid Mechanics (2022), 24:80<\/li>\n
  2. T. Kubo, Y. Shibata, On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface, Mathematics 9 (2021), no.6, 621: https:\/\/doi.org\/10.3390\/math9060621<\/a><\/li>\n
  3. T. Kubo, R. Matsui, On pressure stabilization method for nonstationary Navier-Stokes equations, Communications on Pure and Applied Analysis, 17 (2018), no. 6, 2283\u20132307.<\/li>\n
  4. T. Kobayashi, T. Kubo, K. Nakamura, On a Local Energy Decay Estimate of Solutions to the Hyperbolic type Stokes Equations, Journal of Differential Equations, 264 (2018), no. 10, 6061\u20136081.<\/li>\n
  5. T. Kubo, Y. Shibata, K. Soga,\u00a0On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface<\/a>. Discrete and Continuous Dynamical Systems – Series A,(2016) 3741-3774<\/li>\n
  6. T.Kobayashi, T.Kubo, Weighted Lp-Lq estimates of Stokes semigruoup in half-space and its application to the Navier-Stokes equations, Advances in Mathematical Fluid Mechanics, Recent Developments of Mathematical Fluid Mechanics,(2016). 337-350<\/li>\n
  7. T. Hishida, T. Kubo, On the Asymtotic stability for small initial disturbance of Navier-Stokes flow in a two-dimensional aperture domain, Gakuto International Series, Mathematical Sciences and Application, Mathematical Fluid Dynamics and Nonlinear Wave, (2015) 183-192.<\/li>\n
  8. T. Kobayashi, T. Kubo, Weighted estimates of Stokes semigroup in unbounded domains, Advanced studies in pure mathematics 64, Proceedings for the 4th MSJ-SI conference on Nonlinear Dynamics in Partial Differential Equations, (2015), 427-436<\/li>\n
  9. T. Kubo, Y. Shibata, K. Soga, On the R-boundedness for the two phase problem: compressible-incompressible model problem, Boundary Value Problem, (2014):141, 33pp.<\/li>\n
  10. T. Kobayashi, T. Kubo, Weighted Lp-Lq etimates of the Stokes semigroup in some unbounded domains, Tsukuba J. Math. Vol.37 No.2 (2013).179-205.<\/li>\n
  11. T. Kubo, The Stokes and Navier-Stokes equations in an aperture domain, J. Math. Soc. Japan, Vol.59, No.3 (2007),837-859.<\/li>\n
  12. T. Kubo, On the Stokes and Navier-Stokes equations in a perturbef half-space and an aperture domain, Asymptotic Analysis and Singularities, Hyperbolic and dispersive PDEs and uid mechanics, 47-1, Advanced Studies in Pure Mathematics, T. Kohno et al. ed. Tokyo Shoseki Printing Co. (2007), 169-187.<\/li>\n
  13. T. Kubo and Y. Shibata, Lp – Lq estimate of the Stokes semigroup and its application to Navier-Stokes equation in a perturbed half-space, Hyperbolic Problems, Theory, Numerics and Applications, II, Asakura et al. ed. Yokohama Publishers (2006), 125-132.<\/li>\n
  14. T. Kubo, Periodic solutions of the Navier-Stokes equations in a perturbed half-space and an aperture domain, Mathematical Methods in the Applied Sciences, 28, No.11 (2005), 1341-1357.<\/li>\n
  15. T. Kubo and Y. Shibata, On some properties of solutions to the Stokes equation in the half-space and perturbed half-space. Equations in Math. Physics Quaderni in Mathematica, series edited by Dept. Math. II Univ. di Napoli 15 (2005), 151-220.<\/li>\n
  16. T. Kubo and Y. Shibata, On the Stokes and Navier-Stokes ows in a perturbed half-space, Regularity and Other Aspects of the Navier-Stokes Equations, \u3000Vol. 70, Banach Center Publications (2005), 157-167.<\/li>\n
  17. T. Kubo and Y. Shibata, On the Stokes and Navier-Stokes equations in a perturbed half-space, Advances in Differential Equations, Vol. 10, No.6 (2005), 695-720.<\/li>\n<\/ol>\n

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    1. T. Kubo, Analysis of non-stationary Navier-Stokes equations approximated by the pressure stabilization method, \u7814\u7a76\u96c6\u4f1a”\u975e\u5727\u7e2e\u6027\u7c98\u6027\u6d41\u4f53\u306e\u6570\u7406\u89e3\u6790”,\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u93322107(2019),46-68.<\/li>\n
    2. T. Kubo, On two phase problem: compressible -compressible model problem, \u7814\u7a76\u96c6\u4f1a”\u975e\u5727\u7e2e\u6027\u7c98\u6027\u6d41\u4f53\u306e\u6570\u7406\u89e3\u6790”,\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u93321905(2014),61-72.<\/li>\n
    3. T. Kubo, Weighted Lp -Lq estimate for the Stokes semigroup in half-space and perturbed half-space, \u7814\u7a76\u96c6\u4f1a”\u6d41\u4f53\u3068\u6c17\u4f53\u306e\u6570\u5b66\u89e3\u6790”,\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u93321730 (2011), 1-17.<\/li>\n
    4. T. Kubo, The Stokes and Navier-Stokes equations in an aperture domain, \u7814\u7a76\u96c6\u4f1a”\u6d41\u4f53\u3068\u6c17\u4f53\u306e\u6570\u5b66\u89e3\u6790”, \u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u93321592 (2008), 53-68.<\/li>\n
    5. T. Kubo and Y. Shibata, Lp – Lq estimate of the Stokes semigroup in a perturbed half-space, \u7814\u7a76\u96c6\u4f1a”\u8abf\u548c\u89e3\u6790\u5b66\u3068\u975e\u7dda\u5f62\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f, \u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u93321389(2004),93-119.<\/li>\n<\/ol>\n

      \u6642\u9593\u9045\u308c\u3092\u542b\u3080\u5fae\u5206\u65b9\u7a0b\u5f0f\u95a2\u4fc2<\/h2>\n
        (\u67fb\u8aad\u6709)<\/ol>\n
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        1. T.Kubo, Y. Ueda, Large time behavior of solutions to Burgers equation with a time delay, Communications in Mathematical Analysis and Applications (2025), DOI: 10.4208\/cmaa.2025-0011<\/a>.<\/li>\n
        2. T. Kubo, Y. Ueda, Existence theorem for global in time solutions to Burgers equation with a time delay, Journal of Differential Equations 333 (2022), 184-230.<\/li>\n<\/ol>\n

          \u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u95a2\u4fc2<\/h2>\n

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          1. A.Takayasu, M. Mizuguchi, T. Kubo, and S. Oishi: “Accurate Method of Verified Computing for Solutions of Semilinear Heat Equatinos”, Reliable Computing, Vol.25, (2017), 74-99.<\/li>\n
          2. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:\u00a0“A method of verified computations for solutions to semilinear parabolic equations using semigroup theory”<\/i>, SIAM J. Numer. Anal., Vol.55, No.2(2017)980-1001,<\/li>\n
          3. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi: “Numerical verification for existence of a global-in-time solution to semilinear parabolic equations”, Journal of Computational and Applied Mathematics, 315(2017)1-16.<\/li>\n
          4. M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi:\u00a0“On the embedding constant of the Sobolev type inequality for fractional derivatives”<\/i>, NOLTA, IEICE, Vol.7, No.3(2016), 386-394.<\/li>\n
          5. A. Takayasu, S. Oishi, T. Kubo,Numerical Existence Theorem for Solutions of Two-Point Boundary Value Problems of Nonlinear Differential Equations, NOLTA, IE-ICE, Vol.E93-N, No.10 (2010), 105-118.<\/li>\n
          6. A. Takayasu, S. Oishi, T. Kubo,Computer assisted proofs of solutions to Nonlinear\u3000elliptic partial differential equations, Proceedings of 2010 International Symposium\u3000on Nonlinear Theory and its Applications (NOLTA 2010) (2010),135-138.<\/li>\n
          7. A. Takayasu, S. Oishi, T. Kubo,A priori inverse operator estimation for guaranteed\u3000error estimate, Proceedings of 4th Workshop on Reliable Engineering Computing\u3000(REC2010) “Robust Design – Coping with Hazards, Risk and Uncertainty”,Singapore\u3000(2010), 649-664.<\/li>\n
          8. A. Takayasu, S. Oishi, T. Kubo,Guaranteed error estimate for solutions to two-point boundary value problem, Proceedings of 2009 International Symposium on\u3000Nonlinear Theory and its Applications (NOLTA2009)(2009),214-217.<\/li>\n
          9. A. Takayasu, S. Oishi, T. Kubo,Guaranteed error estimate for solutions to linear\u3000two-point boundary value problems with FEM, Proceedings of ASIA SIMULATION\u3000CONFERENCE 2009 (JSST 2009) (2009), Paper ID: 163.<\/li>\n<\/ol>\n

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              \n
            1. A. Takayasu, S. Oishi, T. Kubo, Numerical Existence Proofs and Guaranteed Error Bounds for Solutions to Two-Point Boundary Value Problems, \u7814\u7a76\u96c6\u4f1a \u6570\u5024\u89e3\u6790\u3068\u6570\u5024\u8a08\u7b97\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6700\u8fd1\u306e\u5c55\u958b,\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240\u8b1b\u7a76\u9332, 1719 (2010), 48-60.<\/li>\n
            2. A. Takayasu, S. Oishi, T. Kubo,Numerical veri cation for solutions to nonlinear two-point boundary value problems with nite element method, Proceedings of the 24th International Technical Conference on Circuits\/Systems, Computers and Communications (ITC-CSCC 2009) (2009), 165-168.<\/li>\n<\/ol>\n

              \u305d\u306e\u4ed6<\/h2>\n
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              1. N. Fukuda, T. Kinoshita and T. Kubo, “On the Galerkin-wavelet method for higher order differential equations, the Bulletin of the Korean Mathematical Society,Vol 50, No.3(2013),963-982.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

                Navier-Stokes\u65b9\u7a0b\u5f0f\u95a2\u4fc2 (\u67fb\u8aad\u6709) H. Kikuchi, T. Kubo, R. Matsui, Existence of Weak Solution to the Navier-Stokes Equat … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a><\/p>\n","protected":false},"author":51,"featured_media":0,"parent":6,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-109","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/users\/51"}],"replies":[{"embeddable":true,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/comments?post=109"}],"version-history":[{"count":6,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/109\/revisions"}],"predecessor-version":[{"id":347,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/109\/revisions\/347"}],"up":[{"embeddable":true,"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/pages\/6"}],"wp:attachment":[{"href":"https:\/\/www-p.sci.ocha.ac.jp\/math-kubo-lab\/wp-json\/wp\/v2\/media?parent=109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}