Local existence of the shock front solution to the axi-symmetrical piston problem in compressible flow (Q705093)

Axi-symmetrical solutions of the two-dimensional Euler equations of a polytropic gas are considered in an expanding domain \(r\geq b(t)\) under the assumption that \(b(0)=0\), \(b' (0)=b_0 >0,\) \(b^{(k)}(0)=0\), \(2\leq k\leq K\), where \(K\) is a given large integer. The initial data are \(u=0\), \(\rho =\) \(\rho_a =\) \(\text{const}>0\). Local time existence of a shock-front solution is proved.