Structure of the solutions to non-linear hyperbolic partial differential equations derived from astrophysics

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03371
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Yamaguchi University
• Principal Investigator: Makino Tetu 山口大学, その他部局等, 名誉教授 (00131376)
• Project Period (FY): 2018-04-01 – 2023-03-31
• 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

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.

Free Research Field

数学

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。