TY - JOUR
T1 - Converging/Diverging Self-Similar Shock Waves
T2 - From Collapse to Reflection
AU - Schrecker, Matthew
AU - Jang, Juhi
AU - Liu, Jiaqi
PY - 2024/9/11
Y1 - 2024/9/11
N2 - We solve the continuation problem for the non-isentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Gu ̈derley imploding shock solutions for a perfect gas with adiabatic exponent $\gamma \in (1, 3]$ admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for $\gamma \in (1, \frac53], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.
AB - We solve the continuation problem for the non-isentropic Euler equations following the collapse of an imploding shock wave. More precisely, we prove that the self-similar Gu ̈derley imploding shock solutions for a perfect gas with adiabatic exponent $\gamma \in (1, 3]$ admit a self-similar extension consisting of two regions of smooth flow separated by an outgoing spherically symmetric shock wave of finite strength. In addition, for $\gamma \in (1, \frac53], we show that there is a unique choice of shock wave that gives rise to a globally defined self-similar flow with physical state at the spatial origin.
M3 - Article
SN - 0036-1410
JO - Siam Journal on Mathematical Analysis
JF - Siam Journal on Mathematical Analysis
ER -