天体物理学中不规则形状的 Euler–Poisson 主导分子云在近边界质量吸积下的爆破与长时间演化
Blowups and longtime developments with near-boundary mass accretions of irregularly-shaped Euler--Poisson dominated molecular clouds in astrophysics
AI总结：
本文研究不规则形状 Euler–Poisson 分子云的长时间演化，证明在容许数据下解要么整体存在并发生近边界质量吸积导致恒星形成，要么在有限时间内爆破，部分回答了 Makino 猜想。
摘要：
受分子云形成恒星这一天体物理问题的启发，我们针对某些不规则形状分子云可能的长时间行为迈出了第一步。我们强调，含真空的不规则形状流体（分子云）的爆破主要困难来自其密度初始不规则构型（多个重心）。这不可避免地导致演化过程中的运动比球对称情形复杂得多。球对称情形已被充分研究。然而，对于带引力的非球对称情形，由于引力与流体之间存在非常复杂的非线性相互作用，文献中极为少见。本文得出结论：在容许数据（即大尺度、不规则形状、膨胀且旋转的分子云）下，解（分子云）的演化要么是整体的（第一类），并伴随近边界质量吸积（导致恒星形成），要么在有限时间内爆破。此外，如果数据是强容许的，某些奇点可以从边界移除。本文部分回答了 Makino 于 1992 年提出的猜想 [37]，该猜想涉及某些数据下无对称性的任意 tame 解的有限时间爆破；分子云模型与局部适定性已在伴随文章 [30] 中建立。
英文摘要：
Motivated by the astrophysical problems of star formations from molecular clouds,we make the first step on the possible long time behaviors of certain irregularly-shaped molecular clouds. We emphasis the main difficulty of the blowups of the irregular-shaped fluids with vacuum (molecular clouds) comes from the initial irregular configurations of its density (multiple centers of gravity). This inevitably causes far more complicated movements during the evolution than the one with spherical symmetry. The spherical symmetric case has been well studied. However, for the non-spherical symmetric case with the gravity, it is very rare in the references due to a very complicate nonlinear interaction between the gravity and the fluids. This article concludes, under the admissible data (i.e., large scale, irregularly-shaped, expanding and rotational molecular clouds), the developments of the solution (molecular clouds) are either global (the first class) with near-boundary mass accretions (leads to star formations), or blowup at finite time. In addition, certain singularities can be removed from the boundary if the data is strongly admissible. This paper partially answers Makino's conjecture [37] in 1992 on the finite time blowup of any tame solution without symmetries for some data and the model of the molecular clouds and the local wellposedness have been established in the companion article [30].
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