Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe

Abstract

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.

arXiv comment21 pages; Introduction and discussion expanded; Typos corrected; agrees with published version

References in corpus (9)

• Jeans analysis of self-gravitating systems in f(R)-gravity
• The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models
• A conformal approach for the analysis of the non-linear stability of pure radiation cosmologies
• Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant
• Why does the Jeans Swindle work?
• Jeans Instability in Classical and Modified Gravity
• Cosmological Newtonian limits on large spacetime scales
• Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
• Future stability of the FLRW spacetime for a large class of perfect fluids

Cited by in corpus (3)

• Fully nonlinear gravitational instabilities for expanding Newtonian universes with inhomogeneous pressure and entropy: Beyond the Tolman's solution
• Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
• Blowups and longtime developments with near-boundary mass accretions of irregularly-shaped Euler--Poisson dominated molecular clouds in astrophysics