Year: 2026
Type: preprint
Abstract: We consider the barotropic Euler equations in dimension $d > 1$ with decaying density at spatial infinity. The phase portrait of the nonlinear ODE governing the equation for spherically symmetric self-similar solutions has been introduced in the pioneering work of Guderley. The existence of smooth decaying solutions through the sonic line has been obtained in the work (F. Merle et al., 2022) in a suitable range of parameters. We work in this paper in a different range of parameters and show the existence of holosphere like solutions which are smooth through the sonic line, but display vanishing density at a sphere.
Source: arXiv (Cornell University)
Author: Kim, Jihoi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204933228