Two Dimensional Subsonic and Subsonic-Sonic Spiral Flows Outside a Porous Body

Weng, Shangkun; Zhang, Zihao

doi:10.1007/s10473-022-0416-1

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Utilizing the compensated compactness, the subsonic-sonic limit to the 2-D or three dimensional axisymmetric steady irrotational flows were proved in [4,36] and later on these results were extended to the multidimensional potential flows and steady Euler flows cases in [5,14]. Subsonic and subsonic-sonic spiral flows outside a porous body were obtained recently in [34]. However, the solutions obtained by the subsonic-sonic limit only satisfy the equations in the sense of distribution and there is no information about the regularity and degeneracy properties near sonic points and their distribution in flow region.…”

Section: Smooth Transonic Flows With Nonzero Vorticity For the Quasi ...mentioning

confidence: 94%

“…In the recent researches, the role played by the angular velocity in the structure of steady inviscid compressible flows for Euler system has been elucidated in [13], and the authors gave a new proof of the existence of smooth transonic spiral flows by studying one side boundary value problem to the steady Euler system in an annulus, which suits their further purpose for the investigation of structural stability of this special transonic flows in [14]. Moreover, [16] established the existence of subsonic spiral flows outside a porous body by a variational method.…”

Section: Transonic Shock Flows In An Annulusmentioning

confidence: 99%

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On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

Weng

Xin

Yuan

2021

Math. Models Methods Appl. Sci.

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This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli’s function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.

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Section: Smooth Transonic Flows With Nonzero Vorticity For the Quasi ...mentioning

confidence: 94%

Section: Transonic Shock Flows In An Annulusmentioning

confidence: 99%

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

Weng

Xin

Yuan

2021

Math. Models Methods Appl. Sci.

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Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model

Weng,

Xin

2024

Arch Rational Mech Anal

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Smooth symmetric transonic isothermal flows with nonzero angular velocity

Zhang

2023

Journal of Mathematical Physics

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In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary conditions at the inner and outer circle. By solving the one side boundary problem, we obtain that there exist accelerating or decelerating smooth transonic flows in an annulus. Moreover, the structural stability of these smooth symmetric transonic flows with nonzero angular velocity are further investigated. Furthermore, we examine the transonic solutions with shocks as well via prescribing suitable boundary conditions on the inner and outer circle.

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Two Dimensional Subsonic and Subsonic-Sonic Spiral Flows Outside a Porous Body

Cited by 3 publications

References 18 publications

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

Smooth Transonic Flows with Nonzero Vorticity to a Quasi Two Dimensional Steady Euler Flow Model

Smooth symmetric transonic isothermal flows with nonzero angular velocity

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