多维辐射流体动力学模型的全局光滑径向对称解
Global Smooth Radially Symmetric Solutions to a Multidimensional Radiation Hydrodynamics Model
AI总结：
本文研究三维有界同心环形区域内辐射 Euler 方程的初边值问题，证明了在初始数据足够小的条件下存在唯一的全局光滑径向对称解。
摘要：
可压缩无粘辐射流的运动可由辐射 Euler 方程描述，该方程由 Euler 系统与关于辐射热通量的 Poisson 方程通过能量方程耦合而成。尽管无论初始数据多么光滑和微小，可压缩 Euler 系统的解通常都会产生奇异性，但人们认为辐射效应确实意味着某种耗散机制，至少对于小初始数据，该机制可以保证辐射 Euler 方程解的全局正则性。这种期望在一维情况下得到了严格验证，但就多维情况而言，据我们所知，目前还没有任何结果。本文的主要目的是证明，在三维有界同心环形区域中，此类辐射 Euler 方程的初边值问题确实存在唯一的全局光滑径向对称解，前提是初始数据足够小。
英文摘要：
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although solutions of the compressible Euler system will generally develop singularity no matter how smooth and small the initial data are, it is believed that the radiation effect does imply some dissipative mechanism, which can guarantee the global regularity of the solutions of the radiative Euler equations at least for small initial data. Such an expectation was rigorously justified for the one-dimensional case, as for the multidimensional case, to the best of our knowledge, no result was available up to now. The main purpose of this paper is to show that the initial-boundary value problem of such a radiative Euler equation in a three-dimensional bounded concentric annular domain does admit a unique global smooth radially symmetric solution provided that the initial data is sufficiently small.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
