Steady compressible subsonic impinging flows with non-zero vorticity

Abstract

A well-posedness analysis of steady state of inviscid compressible subsonic impinging flows with non-zero vorticity is developed. A nonlinear nonhomogeneous second-order partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specifying the horizontal velocity. We first construct a subsonic solution to the impinging flow problem with special horizontal velocity and specific effluent fluxes in the outlets. Moreover, we showed that such a subsonic impinging flow with the same asymptotic behavior in the upstream and downstreams is unique. Furthermore, the existence, uniqueness and regularity of the interface separating the two fluids with different outlets are obtained. This result extends the recent result on the compressible subsonic irrotational impinging flows in [5]. Finally, as a byproduct, we obtain the existence of subsonic-sonic impinging flows.