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Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$

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.

Author Details

Xingli Li

Jianli Liu

Manwai Yuen