|
| Non-Global Existence of Regular Solutionto Initial Value Problem of RelativisticEuler Equations in RN |
| Xingli Li,Jianli Liu,Manwai Yuen |
| (Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Mathematics, Shanghai University, Shanghai 200444, China;
Newtouch Center for Mathematics of Shanghai University, Shanghai
University, Shanghai 200444, China;Department of Mathematics and Information Technology, The Education
University of Hong Kong, Hong Kong, China) |
| DOI： |
| 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 R
N . If
the initial velocity satisfies
max
~x0∈??(0)
N
X
i=1
vi
2
(0,~x0)<
c
2
2
A1
,
where A1 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. |
| Key words: Non-global existence, relativistic Euler equations, regular solution, initial
value problem. |