1998 Fiscal Year Final Research Report Summary
Applied Mathematical Analysis of Fluid Mechanics
| Project/Area Number |
09640227
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | Meiji University |
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Principal Investigator |
MORIMOTO Hiroko School of Science and Technology Professor, 理工学部, 教授 (50061974)
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| 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)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Navier-Stokes equations / Boussinesq equations / stationary solutions / general outflow condition |
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| 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.
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