Subsonic Flows in a Multi-Dimensional Nozzle

Abstract

In this paper, we study the global subsonic irrotational flows in a multi-dimensional ($n\ge 2$) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension for sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow. Furthermore, we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely, provided that the incoming mass flux is less than the critical value. This gives a positive answer to the problem of Bers on global subsonic irrotational flows in infinitely long nozzles for arbitrary dimension. Finally, under suitable asymptotic assumptions of the nozzle, we obtain the asymptotic behavior of the subsonic flow in far fields by a blow-up argument. The main ingredients of our analysis are methods of calculus of variations, the Moser iteration techniques for the potential equation and a blow-up argument for infinitely long nozzles.

to appear in Arch. Rational Mech. Anal

References in corpus (1)

• Global Subsonic and Subsonic-Sonic Flows through Infinitely Long Axially Symmetric Nozzles

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• Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles
• Existence of Steady Subsonic Euler Flows through Infinitely Long Periodic Nozzles
• Three Dimensional Steady Subsonic Euler Flows in Bounded Nozzles
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• Low Mach Number Limit and Far Field Convergence Rates of Potential Flows in Multi-Dimensional Nozzles With an Obstacle Inside
• Steady collision of two jets issuing from two axially symmetric channels
• Oblique Injection of incompressible ideal fluid from a slot into a free stream