带物理真空的可压缩欧拉方程的光滑自相似解
On smooth self similar solution to compressible Euler equation with physical vacuum
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中文总结 AI 辅助
本文针对空间无穷远处密度衰减的高维正压可压缩欧拉方程，在不同于Merle等人的参数范围内，证明了穿过声线光滑但在球面处密度消失的类全向自相似解的存在性。
中文摘要 AI 辅助
我们考虑空间无穷远处密度衰减的d>1维正压欧拉方程。控制球对称自相似解的非线性常微分方程的相图由Guderley的开创性工作引入。Merle等人（2022）的工作已在合适的参数范围内获得了穿过声线的光滑衰减解的存在性。本文在不同的参数范围内研究，证明了类全向解的存在性，该解穿过声线时光滑，但在某一球面上密度消失。
英文摘要
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.
发表机构
- University of Cambridge, United Kingdom（英国剑桥大学）
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