论文标题
在扩展的牛顿宇宙中，严格的非线性牛仔裤不稳定的证明
Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
论文作者
论文摘要
由于欧拉（Poisson方程）的非线性，非线性牛仔裤的不稳定性可能会导致密度增长速度比线性牛仔裤不稳定性的标准理论中的速率更快，这激发了我们研究非线性牛仔裤的不稳定性。本文的目的是开发一种方法，证明了扩展的牛顿宇宙中略微非线性的欧拉 - 波森方程的牛仔裤不稳定性。牛仔裤不稳定性的标准证明取决于傅立叶分析。但是，很难将傅立叶方法概括为非线性设置，因此牛仔裤不稳定性的非线性分析没有结果。首先，我们开发了一种基于非四折的方法，以在不断扩展的牛顿宇宙中谴责线性化牛仔裤的不稳定性。其次，我们将这个想法概括为略有非线性情况。由于该系统在数学方面的最新发展，这种方法依赖于Fuchsian系统的Cauchy问题。 Euler-Poisson和Einstein-Euler方程的完全非线性牛仔裤不稳定性正在进行中。
Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard theory of linearized Jeans instability, which motivates us to study the nonlinear Jeans instability. The aim of this article is to develop a method proving the Jeans instability for slightly nonlinear Euler-Poisson equations in the expanding Newtonian universe. The standard proofs of the Jeans instability rely on the Fourier analysis. However, it is difficult to generalize Fourier method to a nonlinear setting, and thus there is no result in the nonlinear analysis of Jeans instability. We firstly develop a non-Fourier-based method to reprove the linearized Jeans instability in the expanding Newtonian universe. Secondly, we generalize this idea to a slightly nonlinear case. This method relies on the Cauchy problem of the Fuchsian system due to the recent developments of this system in mathematics. The fully nonlinear Jeans instability for the Euler-Poisson and Einstein-Euler equations are in progress.
