TY - JOUR
T1 - Two-Dimensional Steady Supersonic Relativistic Euler Flows Past Lipschitz Wedges
AU - Ding , Min
AU - Li , Yachun
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 314
EP - 348
PY - 2024
DA - 2024/07
SN - 3
DO - http://doi.org/10.4208/cmaa.2024-0013
UR - https://global-sci.org/intro/article_detail/cmaa/23231.html
KW - Steady supersonic relativistic Euler flow, shock wave, rarefaction wave,
wave front tracking method, interaction of waves, asymptotic behavior.
AB - <p style="text-align: justify;">This paper is a review of wedge problems for supersonic relativistic
Euler flows. We are mainly concerned with two-dimensional compressible supersonic relativistic Euler flows past Lipschitz wedges, sharp corners, or bending wedges from mathematical point of view. When the vertex angle of the
upstream flow is less than the critical angle, a shock wave is generated from
the wedge vertex. If the vertex angle is larger than $\pi$ and the angle of the
flow is larger than the critical value, then a rarefaction wave will appear. In
this paper, we employ modified wave front tracking method to establish the
structural stability of such wave patterns under some small perturbations of
both the upcoming supersonic flow and the tangent slope of the boundary. It
is an initial-boundary value problem for two-dimensional steady compressible
relativistic Euler system. Moreover, we study global non-relativistic limits of
entropy solutions for relativistic Euler flows as well as the asymptotic behavior
of the solutions at the infinity. In particular, we demonstrate the basic properties of nonlinear waves for the two-dimensional steady supersonic relativistic
Euler flows, especially, the geometric structures of shock polar and rarefaction
wave.</p>