Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity (Q1795185)

The authors study the Cauchy problem for the 2-dimensional compressible Euler equations. The equation of state is arbitrary, except for the Chaplygin gas state equation. The space is the Cartesian product of \(\mathbb R\) and \([0,1]\) with its ends glued. The main result states that stable finite-time shock solutions are possible, for certain initial data, for any equation of state (except for the Chaplygin gas). Even more, vorticity may be non-zero at the shock.