2022/08/14 by Chao Liu, Liu, Chao · 3 citations
Engineering · Mathematics · #35L10 #83F05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Primary 35A01 #Secondary 35L02
paper · pdf · doi:10.48550/arxiv.2208.06788
openalex publication_date 2022/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. It has been a long-standing open problem in astrophysics for more than a century. In this article, we focus on a reduced model of the nonlinear Jeans instability in an expanding Newtonian universe, which is described by a class of second-order nonlinear hyperbolic equations. \Box \varrho(xμ) +(a )/(t) ∂t\varrho(xμ) - (b)/(t2) \varrho(xμ) (1+ \varrho(xμ) ) -(c-k )/(1+\varrho(xμ)) (∂t\varrho(xμ))2= k F(t). We establish a family of nonlinear self-increasing blowup solutions (where the solution itself becomes infinite in a stable ODE-type blowup) for this equation. Furthermore, we provide estimates on the growth rate of \varrho, which may help explain why the nonlinear structures in the universe grow much faster in astrophysical observations than predicted by the classical Jeans instability.