Volume 40, Issue 3
Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$

Xingli Li, Jianli Liu & Manwai Yuen

Ann. Appl. Math., 40 (2024), pp. 249-261.

Published online: 2024-09

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  • 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.

  • AMS Subject Headings

35A01, 35E15 , 35Q75

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COPYRIGHT: © Global Science Press

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@Article{AAM-40-249, author = {Li , XingliLiu , Jianli and Yuen , Manwai}, title = {Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {3}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0012}, url = {http://global-sci.org/intro/article_detail/aam/23424.html} }
TY - JOUR T1 - Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$ AU - Li , Xingli AU - Liu , Jianli AU - Yuen , Manwai JO - Annals of Applied Mathematics VL - 3 SP - 249 EP - 261 PY - 2024 DA - 2024/09 SN - 40 DO - http://doi.org/10.4208/aam.OA-2024-0012 UR - https://global-sci.org/intro/article_detail/aam/23424.html KW - Non-global existence, relativistic Euler equations, regular solution, initial value problem. AB -

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.

Li , XingliLiu , Jianli and Yuen , Manwai. (2024). Non-Global Existence of Regular Solution to Initial Value Problem of Relativistic Euler Equations in $\mathbb{R}^N$. Annals of Applied Mathematics. 40 (3). 249-261. doi:10.4208/aam.OA-2024-0012
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