2010 Fiscal Year Final Research Report
Maximal regularity theory and its application
| Project/Area Number |
20540164
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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 | Shizuoka University |
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Principal Investigator |
SHIMIZU Senjo Shizuoka University, 理学部, 教授 (50273165)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUCHI Koji 静岡大学, 工学部, 教授 (50195202)
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| Co-Investigator(Renkei-kenkyūsha) |
OGAWA Takayoshi 東北大学, 理学研究科, 教授 (20224107)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 最大正則性 / 自由境界問題 / ナビエ-ストークス方程式 / R-有界性 / フーリエ・マルチプライヤーの定理 |
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| Research Abstract |
We develop the method to prove maximal regularity by proving R-bounded of an solution operator in view of operator-valued Fourier-multiplier theorem. As an application of the maximal regularity, we prove local solvability of free boundary problems for the Navier-Stokes equations with surface tension in a scale invariant Sobolev space. Moreover we prove maximal regularity of the Cauchy problem for the heat equation in homogeneous Besov space that is not a UMD (unconditional martingale differences) Banach space.
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