Global Existence of a Solution for Isentropic Gas Flow in the Laval Nozzle with a Friction Term

Tsuge, Naoki

doi:10.1137/21m1415029

SIAM J. Math. Anal.

2022

DOI: 10.1137/21m1415029

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Global Existence of a Solution for Isentropic Gas Flow in the Laval Nozzle with a Friction Term

Naoki Tsuge¹

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Cited by 3 publications

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“…As for the problems in the Laval nozzle and the general nozzle, we can see [2,31,32] and the references in. While, for the problems on damped isentropic gas flow in nozzles, we refer to [20,29,30,33] for the existence of the global weak entropy solutions. However, there are few studies on non-isentropic gas dynamics systems in ducts with variable cross-sectional areas and frictions.…”

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confidence: 99%

Flow in ducts with varying cross-sectional area and friction

Ma,

Sun,

2024

DCDS-S

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In this paper, we study the non-isentropic compressible Euler equations in ducts with varying cross-sectional area and friction. We analyze the combined effect of cross-sectional area and friction subtly and investigate the motion trend of the corresponding steady flow along ducts. Moreover, for the time-dependent system, when the boundary perturbations are temporal-periodical, we can utilize an energy function and Gronwall's inequality to demonstrate that the smooth supersonic solution is a temporal periodic solution, after a certain start-up time, possessing the same period as the boundary conditions. The semi-global existence of a C 1 solution to the mixed initial-boundary value problem is used in the proof.

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confidence: 99%

Flow in ducts with varying cross-sectional area and friction

Ma,

Sun,

2024

DCDS-S

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Global existence of classical solutions for the gas flows near vacuum through ducts expanding with space and time

Chou

Hong

Lee

2023

Journal of Mathematical Analysis and Applications

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Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects

Fang,

Ma,

2024

Advances in Nonlinear Analysis

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In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to x x into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.

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Global Existence of a Solution for Isentropic Gas Flow in the Laval Nozzle with a Friction Term

Cited by 3 publications

References 6 publications

Flow in ducts with varying cross-sectional area and friction

Flow in ducts with varying cross-sectional area and friction

Global existence of classical solutions for the gas flows near vacuum through ducts expanding with space and time

Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects

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