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 -