| Project/Area Number |
24340025
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University (2016)
Shizuoka University (2012-2015) |
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Principal Investigator |
Shimizu Senjo 京都大学, 人間・環境学研究科(研究院), 教授 (50273165)
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| Co-Investigator(Kenkyū-buntansha) |
田中 直樹 静岡大学, 理学部, 教授 (00207119)
菊地 光嗣 (菊池 光嗣) 静岡大学, 工学部, 教授 (50195202)
小林 孝行 大阪大学, 基礎工学研究科, 教授 (50272133)
久保 隆徹 筑波大学, 数理物質科学研究科(系), 講師 (90424811)
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| Co-Investigator(Renkei-kenkyūsha) |
OGAWA Takayoshi 東北大学, 大学院理学研究科, 教授 (20224107)
KUMURA Hironori 静岡大学, 理学部, 准教授 (30283336)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥13,910,000 (Direct Cost: ¥10,700,000、Indirect Cost: ¥3,210,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
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| Keywords | 数学解析 / Navier-Stokes方程式 / 自由境界問題 / 最大正則性 / 相転移 / 適切性 / 安定性 / 非圧縮性粘性流体 / 2相流体 / Lp適切性 / 表面張力 / 端点最大正則性 / 放物型方程式 / ベソフ空間 / ２相問題 / 熱力学平衡 / 平衡解 / コンパクト性 |
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| Outline of Final Research Achievements |
We study the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases. We employ the direct mapping approach to transform the problem locally in time to a fixed domain. The proof of local well-posedness is based on maximal regularity of the underlying principal linearization and the contraction mapping principle. We extend our well-posedness result to general geometries, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exist globally, and if its limit set conatins a stable equilibrium it converge to this equilibrium as time goes to infinity.
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