Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$
Year: 2024
Author: Xingli Li, Jianli Liu, Manwai Yuen
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 249–261
Abstract
In fluid mechanics and astrophysics, relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations. In this paper, we will consider the initial value problem of relativistic Euler equations in an initial bounded region of $\mathbb{R}^N.$ If the initial velocity satisfies $$\max\limits_{\vec{x_0}\in ∂Ω(0)}\sum\limits_{i=1}^N v^2_i(0,\vec{x_0})<\frac{c^2A_1}{2},$$ where $A_1$ is a positive constant depend on some sufficiently large $T^∗,$ then we can get the non-global existence of the regular solution for the $N$-dimensional relativistic Euler equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0012
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 249–261
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Non-global existence relativistic Euler equations regular solution initial value problem.