Steady subsonic potential flows through infinite multi-dimensional largely-open nozzles

Liu, Li; Yuan, Hairong

doi:10.1007/s00526-012-0570-8

Cited by 18 publications

(5 citation statements)

References 18 publications

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“…The uniqueness of symmetric subsonic solutions to potential flows in infinite conical nozzles had been proved in [22] by applying Harnack inequalities, see also [20] for the uniqueness result of the case that M = T 2 . The existence of isentropic irrotational subsonic flows in general three-dimensional largely-open nozzles was proved in [23], while the same existence problem for the three-dimensional Euler system still remains open. See [6] and references therein for some results on subsonic flows in strip-like domains for the two-dimensional compressible Euler system.…”

Section: 3mentioning

confidence: 99%

Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations

Liu

Yuan

2016

Advances in Mathematics

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Section: 3mentioning

confidence: 99%

Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations

Liu

Yuan

2016

Advances in Mathematics

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“…The respective incompressible case is considered in [20]. For the subsonic flow problem in nozzles, one may referee to [8,10,11,16,19,22,25,26].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Two dimensional subsonic and subsonic-sonic spiral flows outside a porous body

Weng¹,

Zhang²

2021

Preprint

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In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flows are obtained via variational formulation. The optimal decay rate at far field is also derived by the Kelvin's transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compactness framework.

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“…Recently, L. L. Du et al [12,14] used this variational approach to study impinging subsonic jets and collision of two subsonic flows. There are also many works on irrotational and rotational subsonic flows past profiles or in nozzles, which are formulated as fixed boundary problems, and we refer to [5,6,11,13,15,16,18,28,34,35,36] and the references therein. Continuous subsonic-sonic flows in convergent nozzles was studied in [29,30,31,32,33], where the flows are governed by free boundary problems of a degenerate elliptic equation, and the sonic curve is a free boundary where the flow velocity is along the normal direction.…”

Section: Introductionmentioning

confidence: 99%

On an Elliptic Free Boundary Problem and Subsonic Jet Flows for a Given Surrounding Pressure

Wang¹,

Xin²

2019

SIAM J. Math. Anal.

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This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic equation. For a given surrounding pressure and a given incoming mass flux, we seek a subsonic jet flow with the given incoming mass flux such that the flow velocity at the inlet is along the normal direction, the flow satisfies the slip condition at the wall, and the pressure of the flow at the free boundary coincides with the given surrounding pressure. In general, the free boundary contains two parts: one is the particle path connected with the wall and the other is a level set of the velocity potential. We identify a suitable space of flows in terms of the minimal speed and the maximal velocity potential difference for the well-posedness of the problem. It is shown that there is an optimal interval such that there exists a unique subsonic jet flow in the space iff the length of the nozzle belongs to this interval. Furthermore, the optimal regularity and other properties of the flows are shown.

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Steady subsonic potential flows through infinite multi-dimensional largely-open nozzles

Cited by 18 publications

References 18 publications

Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations

Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations

Two dimensional subsonic and subsonic-sonic spiral flows outside a porous body

On an Elliptic Free Boundary Problem and Subsonic Jet Flows for a Given Surrounding Pressure

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