Structure of the solutions to non-linear hyperbolic partial differential equations derived from astrophysics
| Project/Area Number |
18K03371
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Yamaguchi University |
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Principal Investigator |
Makino Tetu 山口大学, その他部局等, 名誉教授 (00131376)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2018: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Keywords | 星の内部構造 / Euler-Poisson方程式 / 軸対称計量 / Einstein-Euler方程式 / 気体星の振動モード / 気体星の非動径振動 / 軸対称回転星 / アインシュタイン方程式 / 軸対称重力場 / 非線型偏微分方程式 / 宇宙物理学 |
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| Outline of Final Research Achievements |
Astrophysical study of hydrodynamical structure and evolution of stars is important. Through this study project, the following results have been obtained: (1) As for model of gaseous star in the non-relativistic framework, the spectral analysis of the linearized operator for barotropic perturbations around spherically symmetric equilibrium has been done successfully. (2) As for model of gaseous star in the non-relativistic framework, the existence of a sequence of eigenvalues which accumulates to 0 (so called “g-modes”) of the linearized operator for adiabatic, but not barotropic, perturbations around spherically symmetric equilibrium has been proved. (3) As for metric generated by uniformly, slowly rotating gaseous mass in the general relativistic framework, the existence of asymptotically flat global axisymmetric metric has been proved.
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| Academic Significance and Societal Importance of the Research Achievements |
宇宙物理学から出典する流体力学的問題について、従来不十分であった数学的に厳密な取り扱いを発展させることは、あらたな数学的技法を生み出し、いっぽうまた物理的諸現象の総合的理解を深めるという学術的意義がある。また、宇宙開発などの社会的に重要な科学技術の応用にたいして理論的基盤を与えることになる。
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Report
(6 results)
Research Products
(23 results)
