TY - JOUR
T1 - Local Classical Solutions to the Equations of Relativistic Hydrodynamics
AU - Yipeng Shi 
JO - Journal of Partial Differential Equations
VL - 3
SP - 193
EP - 206
PY - 2001
DA - 2001/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5479.html
KW - Relativistic hydrodynamics
KW - convex entropy
KW - local classical solution
KW - nonrelativistic limit
AB -  In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.