2013 Fiscal Year Final Research Report
Free boundary problems of flows - kinematic undercooling and instability -
| Project/Area Number |
23654048
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
SHIMIZU Senjo 静岡大学, 理学(系)研究科(研究院), 教授 (50273165)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 相転移モデル / 過冷却 / Navier-Stokes方程式 / 2相問題 / 自由境界問題 / 表面張力 / マランゴニ力 / 最大正則性 |
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| Research Abstract |
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics is extended to the case of temperature-dependent surface tension and kinematic undercooling. We prove well-posedness in an Lp-setting, 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 contains a stable equilibrium it converges to this equilibrium as time goes to infinity, in the natural state manifold for the problem.
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