Global uniqueness of steady subsonic Euler flows in three-dimensional ducts

ABSTRACT

We show for certain boundary conditions, under suitable assumptions on the velocity field, the steady compressible Euler flows in three-dimensional straight ducts must be irrotational, and hence, prove global uniqueness of uniform subsonic flows in these ducts. The proof depends on careful analysis of transport equations of vorticity and theory of second-order elliptic equations in bounded or unbounded domains.

Keywords:

• Subsonic flow
• Euler system
• duct
• uniqueness
• elliptic-hyperbolic composite-mixed type

AMS Subject Classifications:

• 35M32
• 35A02
• 76G25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Gang Xu is supported by National Natural Science Foundation of China (NNSFC) [grant number 11571141], [grant number 11371189], [grant number 11271164]; Hairong Yuan is supported by the NNSFC [grant number 11371141], and by Science and Technology Commission of Shanghai Municipality (STCSM) [grant number 13dz2260400].