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 - <p style="text-align: justify;">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 $$\max\limits_{\vec{x_0}\in ∂Ω(0)}\sum\limits_{i=1}^N v^2_i(0,\vec{x_0})&lt;\frac{c^2A_1}{2},$$ 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.</p>