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1999 Fiscal Year Final Research Report Summary

Study on Navier-Stokes equations and related nonlinear partial differential equations

Research Project

Project/Area Number 10440055
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionMeiji University (1999)
Tohoku University (1998)

Principal Investigator

MASUDA Kyuya  Meiji University, Dept. of Science and Technology, Professor, 理工学部, 教授 (10090523)

Co-Investigator(Kenkyū-buntansha) HASEGAWA Fumio  Meiji Univ. Department of Math., Prof., 理工学部, 教授 (70061926)
KONNO Reiji  Meiji Univ. Department of Math., Prof., 理工学部, 教授 (20061921)
MORIMOTO Hiroko  Meiji Univ. Department of Math., Prof., 理工学部, 教授 (50061974)
KATSURADA Masashi  Meiji Univ. Department of Math., Assoc. Prof., 理工学部, 助教授 (80224484)
KANEKO Satiomi  Meiji Univ. Department of Math., Assoc. Prof., 理工学部, 助教授 (20061947)
Project Period (FY) 1998 – 1999
KeywordsNavier-Stokes equations / Magnetic fluid / Reaction-Diffusion equations
Research Abstract

(1) Masuda's Results : He could show the existence of solutions of Navier-Stokes equations in continuous function space.
(2) The result of Masuda and Kenmotsu : They could classify completely the minimal surfaces of constant Gaussian curvature in two-dimensional complex form.
(3) Morimoto's results : she could show the existence of solutions of two dimensional stationary Navier-Stokes equations with general outlet boundary with general outlet boundary condition forsome symmetric domain. Also, she could show the existence of solutions for stationary Boussinesq equations with general outlet boundary condition.
(4) Tani's results : he could show the classical solvability of the Stefan problem in a viscous incompressible fluid flow. Also, he could solve a free boundary problem for an incompressible ideal fluid in two space dimensions.
(5) The result of Ishimura and Nakamura : They could show the convergence of attracters for simplified magenetic Benard system.

  • Research Products

    (41 results)

All Other

All Publications (41 results)

  • [Publications] K.Masuda: "On minimal surfaces of constant curvature in two-dimensional complex form"Journal fuer die Reine und Gewandte Mathematik(Crelles Journal). 519. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Masuda: "Non-existence of nontrivial solution of some nonlinear elliptic equations"Nonlinear Analysis, T.M.A.. (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morimoto: "General outfow condition for Navier-Stokes flow"Lecture Notes in Numerical and Applied Analysis. 16. 209-224 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] "Remarks on the blow-up criterion for the 3D Bousinesq equaitons"Math ; Models Meth.Appl.Sci.. 9. 1323-1332 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] R.Konno: "Growth estimate of generalized eigenfunctions of △ on two-dimensional manifolds"Tech.Rep.School Sci. Eng. Meiji Univ.. 19. 65-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Ishimura: "On the interior blow-up for the curvature evolution of capillary surfaces"Proc. Amer. Math, Soc.. 126. 835-840 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Ishimura: "Self-fimilar solutions for the Gauss curvature evolution of rotationally symmetric surfaces"Nonlinear Analysis T.M.A.. 33. 97-104 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Ishimura: "Shape of spirals"Tohoku Math. J.. 50. 197-202 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Ishimura: "On the structure of steady solutions for the kinematic model of spiral waves in excitable media"Japan J.Indust. Appl. Math. 15. 317-330 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Ishimura: "Motion of spirals by crystalline curvature"Math.Madel Num.Anal.. 33. 797-806 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Nakamura: "Characterization on the long time behavior of the 2D Navier-Stokes equations"Pitman Research Notes in Mathematics. 388. 317-330 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Nakamura: "Convergence of fractal dimension of attractors for the simplified magnetic Benard system"Gakuto Int'l Series Math.Sci.Appl.. 11. 73-81 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Takagi: "On the location and profile of spike-layer solitions to a singularly perturbed semilinear Dirichret problems"Duke Math Journal. 94. 597-618 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Kenmotsu: "The classification of the surfaces with parallel mean curvature vector in two dimensional complex space form"Amer.J.Math. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 増田久弥: "応用解析学"シュプリンガー東京. 600 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Masuda: "Non-existence of non-trivial solutions for some nonlinear Lapalace Equations"in Nonlinear Analysis, T.M.A.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition, Navier-Stokes Rquations and Related Nonlinear Probless"Proc. Of Sixth International Conference NSEC6, Palang, Lithuania, 22-29, Ed. Amann, Galdi, Pileckas, Solonnikov, 22-29, VSP BV & TEV. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Morimoto: "Perturbation of the Boussinesq flow in an annular domain with general outlet condion"Proc. Of International Conference on Navier-Stokes Eqations : Theory and Numerical Methods, Ed. Salvi, Pitmann Research Series 388, 67-75, Adison Wesley Longmann. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Morimoto: "General outflow condition for Navier-Stokes flow"Lecture Note in Numerical Applied Analysis 16 ed. Kozono and Shibata. 209-224 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Morimoto: "Remarks on the blow-up criterion for 3D Boussinesq equations"MAS. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] R. Konno: "Growth estimate of generalized eigenfunctions fo the Laplacian on two dimensional manifolds"Tech. Rep. School Sci. Eng. Meiji Univ. 19. 65 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] R. Konno: "A remark on the Schroedinger-type equation o manifolds, I"Tech. Rep. School Sci. Eng., Meiji Univ. 20. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I. Takagi: "Stability of spiky patterns in an activator-inhibitor system. Proc. Of the Workshop : Nonlinear Partial Differential Equaitons and Related Topics (ed. Ei, Jimbo and others)"Joinsta Center for Sci. and Tech. Of Ryukoku Univ.. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I. Takagi, W. Ni and J. Wei: "of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem : Intermidiate solutions"Duke Math. J. 94. 597-618 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Kenmotsu and K. Masuda: "On minimal surfaces fo constant curvature in two dimensional comples space forms"J. reine angew. Math, (Crelle's Journal). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Kenmotsu and K. Masuda: "The classification of the surfaces with parallel mean curvature vector in two dimensional complex space forms"Amer. J. Math. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Tani: "Pattern formation of spatially discrete Cahn-Hilliard equation"RIMS Lecture Notes. 1040. 188-195 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Tani: "On a free boundary problem for an incompressible ideal fluid in two space dimensions"Advances in Math. Sci. Appl.. 39. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Tani: "On the classical solvability of the Stefan problem in a viscous incompressible fluid flow"SIAMJ. Math. Anal. 30. 584-602 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Tani: "Solvability of nonstationary problems for nonhomogeneous incompressible fluids and the convergence with vanishing viscosity"Tokyo J. Math. 22. 17-42 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura and M. Nakamura: "Convergence of fractal dimension of attracters for the simplified Magnetic Benard system. Recent Development in Domain Decomposition Method, Gakuto International Series"Mathematical Science and Application. 1. 73-81 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Nakamura: "Numerical analysis of Eguchi-Oki-Matsumura equations"Proceedings of Fouth Japan-China Joint Seminar on Numerical Mathematics, Gakuto International Series, Mathematical Science and Applications. 12. 213-222 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura (with Asai, N.): "On the blow up for the curvature of capillary surface"Proc. Amer. Math. Proc.. 126. 835-840 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "Selfsimilar soutions for the Gauss curvature evolution of rotationally symmetric surfaces"Nonlinear Anal. Tm M. A.. 33. 97-104 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "Shape of Spirals"Tohoku J. Math. 50. 197-202 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "On the structure of steady solutions for the kinematic mode of spiral waves in excitabhle media"Japan J. Indust. Appl. Math. 15. 317-330 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura (with M. Nakumura): "Characterization on the long time behavior of the 2D Navier-Stokes equations"Pitman Research Mptes in Mathematics. 388. 38-44 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "Motion ofspirals by crystalline curvature"Math. Model Num, Anal.. 33. 797-806 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "Remarks on the blow-up criterion for the Boussinesq equations"Math Models Meth. Appl. Sci.. 9. 1323-1332 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Ishimura: "A crystalline motion of spiral shaped curves with symmetry"J. Math. Anal. 240. 115-127 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Tachizawa: "Pseudodifferential operators. Gabor frame, and local trigonometric bases"H. Feichtinger and T. Strohmer ed. Gabor analysis and a;gprotjms : Theory and Applications, Birkhauser. 171-192 (1998)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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