On the implosion of a compressible fluid II: Singularity formation

• 成果类型: Article
• 署名作者: Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.196.2.4
• 发表日期: 2022
• 页码: 779-889
• 关键词: blow-up; wave-equation

摘要

In this paper, which continues our investigation of strong singularity formation in compressible fluids, we consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is the existence of C-infinity smooth self-similar solutions to the compressible Euler equations for quantized values of the speed constructed in our companion paper (part I). All blow up dynamics obtained for the Navier-Stokes problem are of type II (non self-similar).