2017 Fiscal Year Final Research Report
Mathematical analysis of motions of some self-gravitating fluids from astronomical phenomena
| Project/Area Number |
26800071
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | University of Miyazaki |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 天体の連続体モデル / 圧縮性粘性流体 / 自己重力 / 自由境界問題 / 球対称運動 |
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| Outline of Final Research Achievements |
Some astronomical phenomena, stellar structure, and so on, was mathematically analyzed by modeling them on the basis of the equations of fluid mechanics. Our main two results are: (1) On the case that the star is composed by a ideal gas and its motion is spacially n-dimensional (n is greater than three), we obtained a certain sufficient condition guaranteeing the long-time existence of the solution of the problem with suitable smoothness and stability, from the initial data with suitable smoothness and without the restriction of the size. (2) We considered an another problem under the situation of (1), in which an additional phenomenon was admitted: the flow of heat through the surface of the star. However on this problem we could not attain the complete result during this study period.
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| Free Research Field |
数物系科学
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