2000 Fiscal Year Final Research Report Summary
Functional-analytic study on incompressible viscous fluid flows
| Project/Area Number |
10440045
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
MIYAKAWA Tetsuro Kobe University Faculty of Science Professor, 理学部, 教授 (10033929)
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| Co-Investigator(Kenkyū-buntansha) |
ADACHI Tadayoshi Kobe University Faculty of Science, Lecturer, 理学部, 講師 (30281158)
FUKUYAMA Katsushi Kobe University Faculty of Science, Associate Professor, 理学部, 助教授 (60218956)
HIGUCHI Yasunari Kobe University Faculty of Science, Professor, 理学部, 教授 (60112075)
HISHIDA Toshiaki Niigata University Faculty of Engineering Lecturer, 工学部, 講師 (60257243)
WATANABE Kiyoshi Kobe University Faculty of Science, Associate Professor, 理学部, 助教授 (60091245)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Navier-Stokes equations / Initial-boundary value problem / Stability / Asymptotic behavior / Limit theorems / Spectral analysis |
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| Research Abstract |
MIYAKAWA deduced the space-time asymptotic profiles in terms of some Gaussian functions for a specific class of solutions of nonstationary Navier-Stokes equations in the whole space and the half-space, and then applied the results to finding a lower bound of rates of energy decay for general weak solutions. HISHIDA considered flows around a rotating body. He developed perturbation theory for the linearized operator and applied it to finding local-in-time solutions for every square-summable initial data. ADACHI developed spectral analysis for quantum many-body Hamiltonians which have stuctures similar to the above-mentioned linearized operator. His result is concerned with systems involving charged and uncharged particles. FUKUYAMA considered the problem of finding limit distributions for discrete dynamical systems arising from the study of lacunary trigonometric series. He deduced a non-Gaussian limit distribution.
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