2010 Fiscal Year Final Research Report
Mathematical Study of Renormalization Groups and applications to Dynamical System
| Project/Area Number |
20540221
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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 |
Global analysis
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| Research Institution | Setsunan University |
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Principal Investigator |
ITO KeiichiR. Setsunan University, 理工学部, 教授 (50268489)
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| Co-Investigator(Kenkyū-buntansha) |
TERAMOTO Yoshiaki 摂南大学, 理工学部, 教授 (40237011)
SHIMADA ShinーIchi 摂南大学, 理工学部, 准教授 (40196481)
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| Co-Investigator(Renkei-kenkyūsha) |
HIROKAWA Masao 岡山大学, 自然科学研究科, 教授 (70282788)
HIROSHIMA Humio 九州大学, 数理科学研究科, 准教授 (00330358)
TAMURA Hiroshi 金沢大学, 理工学部, 教授 (80188440)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 繰りこみ群 / 相転移 / 臨界現象 / 非線形方程式 / 流体 / 乱流 / リッチ・フロウ |
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| Research Abstract |
Ito studied applications of renormalization group method in mathematical sciences from various points of view. He investigates the Ricci flows from statistical mechanics point of view, and suggested that the transformation of manifolds by the flow is strongly related to the Pirogov-Sinai theory of phase transitions.
He also reconsidered the paper by Ya Sinai and D.Li on the constructions of (complex) turbulent solution of Navier-Stokes equation of fluid, using the renormalization group type argument. It seems that the paper needed some calculations to be understood. Ito studied quark confinement problem some decades ago, and established confinement in the hierarchical approximation of the Migdal-Kadanov type. However there appeared a misleading paper in which the author claimed that he established the confinement.
Ito and Prof.E.Seiler of MaxPlanck Institute argued how and why he made mistakes in his arguments.
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