2007 Fiscal Year Final Research Report Summary
REGULARITY ANALYSIS OF DISCRETE MORSE FLOWS FOR ANARISYS OF GENERAL CRITICAL POINTS
| Project/Area Number |
18540192
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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 |
Basic analysis
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| Research Institution | Chiba Institute of Technology |
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Principal Investigator |
HOSHINO Keisuke Chiba Institute of Technology, FACULITY OF ENGINEERING, LECTURER (70327162)
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| Co-Investigator(Kenkyū-buntansha) |
MISAWA Masashi KUMAMOTO UNIVERSITY, FACULITY OF SCIENCE, PROFESSOR (40242672)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Morse flow / discrete Morse flow / harmonic map / local metric manifold / Navier-Stokes equation |
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| Research Abstract |
1. In study on variational problem of harmonic maps between nonsmooth manifolds, in the case of a target manifold with upper bounded curvature, K.Hoshino showed a relaxed version of Alexandrov's NPC inequality to hold also in positively curved manifolds, and apply it for proving a maximal principle and a local estimate for discrete Morse flows. These results assume bounds for radius of initial data, whereas a bound for the local estimate is half of that for the maximum principle, and we constructed Morse flow assuming the smaller bound. We prepare to publish the result and shall continue the research to remove the strong restriction on bounds for initial data.
2. M. Misawa and Takayoshi Ogawa proved a regularity criteria by mean oscillation of harmonic heat flow from manifold into a sphere and published the result in Calculus of Variations and Partial Differential Equations.
3. N. Kikuchi and G. Seregin constructed solutions to nonstationary Navier-Stokes equations satisfying the local energy inequality. They carry on construction and local estimate of solutions to Stokes equations in a special Morrey space and prepare to publish the result.
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[Presentation] A regularity of the hamonic map flow2008
Author(s)
Masashi Misawa
Organizer
Navier-Stokes equations and related topics, KOSEF-JSPS Joint Research and Seminar Project
Place of Presentation
Sungkyonkwan Univ.,Suwon,Korea
Year and Date
2008-01-15
Description
「研究成果報告書概要(和文)」より
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[Presentation] A regularity of the harmonic map flow2008
Author(s)
Masashi, Misawa
Organizer
Navier-Stokes equation and related topics, KOSEF-JSPS Joint Research and Seminor Project
Place of Presentation
Sungkyonkwan Univ., Suwon, Korea
Year and Date
2008-01-15
Description
「研究成果報告書概要(欧文)」より
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