Multidimensional contact discontinuities for inviscid compressible flows

DoctorWe prove the existence of a subsonic weak solution to steady Euler system in a multidimensional nozzle of infinite length when prescribing the value of the entropy at the entrance by a piecewise $C^2$ function with a discontinuity. Due to the variable entropy condition with a discontinuity at the entrance, the corresponding solution has a nonzero vorticity and contains a contact discontinuity. We construct such a solution via Helmholtz decomposition and analyze the asymptotic behavior of the solution at far field