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1998 Fiscal Year Final Research Report Summary

Applied Mathematical Analysis of Fluid Mechanics

Research Project

Project/Area Number 09640227
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionMeiji University

Principal Investigator

MORIMOTO Hiroko  School of Science and Technology Professor, 理工学部, 教授 (50061974)

Co-Investigator(Kenkyū-buntansha) SAITO Norikazu  School pf Science and Technology Assistant, 理工学部, 助手
KATURADA Masashi  School of Science and Technology Lecturer, 理工学部, 教授 (80224484)
KONNO Reiji  School of Science and Technology Professor, 理工学部, 教授 (20061921)
FUJITA Hiroshi  School of Science and Technology Professor, 理工学部, 教授 (80011427)
Project Period (FY) 1997 – 1998
KeywordsNavier-Stokes equations / Boussinesq equations / stationary solutions / general outflow condition
Research Abstract

The existence of solutions to the stationary Navier-Stokes equations is known, in general context, only under the stringent outflow condition or for small Raynolds number. We studied the existence of solutions to the stationary Navier-Stokes equations and of the Boussinesq equations under general outflow condition. We obtained two kinds of results. For arbitrary space dimension and for the boundary value of constant p times gradient of harmonic function, the existence of solution for the above equations is shown except for at most discrete countable case of p. It is to be noted that p can be arbitrary large.
For two dimensional case, under the assumption of symmetry, Amick showed the exis tence of solutions. Fujita obtained the concrete construction of the solenoidal symmetric extension of the boundary value in this case. Using this method, Morimoto and Fujita obtained the existence of solutions to the stationary Navier-Stokes equations in a tube-like domain with inflow and outflow.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 森本浩子: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition." Proceedings of NSEC. 6. 183-193 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimoto, Hiroko with S.Ukai.: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition." Pitmann Research Series. 388. 67-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 森本浩子: "General outflow condition for Navier-Stokes flow," Lecture Note in Numerical and Applied Analysis. 16. 209-224 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimoto, Hiroko with N.Ishimura: "Remarks on the blow-up criterion for 3D Boussinesq equations" M^3AS9(9). to appear. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田宏: "On stationary solutions to Navier-Stokes equation in symmetric plane domains under general outflow condition" Pitmann Research Series. 388. 16-30 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 今野礼二: "Growth estimate of generalized eigenfunctions of △ on two dimensional manifolds." 明治大学理工学部研究報告. 19. 65-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita, H.Morimoto and H.Okamoto: "Stability analysis of the Navier-Stokes flows in annuli" Mathematical Methods in the Applied Sciences. vol.20. 959-978 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita and H.Morimoto: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto International Series Mathematical Science and Applications. Vol.10. 53-61 (1997)

    • 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" Proceedings of NSEC6, Ed.Amann, Galdi, Pileckas, Sol-lonikov. 183-193 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto and S.Ukai: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Navier-Stokes Equations : theory and numerical meth-ods, Ed.R.Salvi, Pitmann Research Series 388. 67-75 (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 Nu-merical and Applied Analysis 16, Recent topics on mathematical theory of viscous incompressible fluid. 209-224 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto and N.Ishimura: "Remarks on the blow-up criterion for 3D Boussinesq equations" (to appear M^3AS9(9). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "On stationary solutions to Navier-Stokes equation in symmetric plane do-mains under general outflow condition" Navier-Stokes Equations : theory and numer-ical methods, Ed.R.Salvi, Pitmann Research Series 388. 16-30 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] R.Konno: "Growth estimate of generalized eigenfunctions of DELTA on two dimensional manifolds" Research Reports School of Science and Technology Meiji University. No.19. 65-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Katurada: "A mathematical study of the charge simulation method using conformal mappings" Memoirs of the Institut of Science and Technology Meiji University. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita, M.Fukuhara and N.Saito: "On the rate of convergence in domain de-composition methods" Proceedings of the third China-Japan seminar on numerical mathematic.30-43 (1998)

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

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Published: 1999-12-08  

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