Self-similar solutions of the relativistic Euler system with spherical symmetry

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-10-24 DOI:10.1090/qam/1680

Bing-Ze Lu, Chou Kao, Wen-Ching Lien

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引用次数: 0

Abstract

We consider the spherical piston problem in relativistic fluid dynamics. When the spherical piston expands at a constant speed, we show that the self-similar solution with a shock front exists under the relativistic principle that all velocities are bounded by the light speed. The equation of state is given by P = σ 2 ρ P= \sigma ^2 \rho , where σ \sigma , the sound speed, is a constant. It is an important model describing the evolution of stars. Also, we present the global existence of BV solutions for the relativistic Euler system given that the piston speed is perturbed around a constant in a finite time interval. The analysis is based on the modified Glimm scheme and the smallness assumption is required on the initial data.

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具有球对称的相对论欧拉系统的自相似解

考虑了相对论流体力学中的球形活塞问题。当球形活塞以恒定速度膨胀时，在所有速度都以光速为界的相对论原理下，我们证明了具有激波前缘的自相似解的存在。状态方程为P= σ 2 ρ P= \sigma ^2 \rho，其中σ \sigma，声速，是一个常数。它是描述恒星演化的一个重要模型。同时，我们给出了当活塞速度在有限时间间隔内绕一个常数扰动时相对论欧拉系统的BV解的整体存在性。该分析基于改进的Glimm格式，对初始数据进行了较小的假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.