Steady compressible subsonic impinging flows with non-zero vorticity

https://doi.org/10.1016/j.jde.2019.09.038Get rights and content
Under an Elsevier user license
open archive

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.

MSC

35Q31
35J25
76G25
76N10

Keywords

Compressible impinging flows
Vorticity
Existence
Uniqueness
Free interface

Cited by (0)

This work is supported in part by NSFC grant 11571243, 11622105, 11971331.