On a regularity result for the transonic pressure-gradient system in gas dynamics

Song, Huijuan; Hu, Yanbo

doi:10.1016/j.jmaa.2019.123495

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2024

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“…The regularity results obtained for isentropic Euler system in [16] were improved by Hu et al in [18]. For more details on ongoing research on two-dimensional Euler system and related models, we refer the reader to [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. All the above works are based on the beautiful concept of characteristic decomposition initiated in the work of Dai and Zhang [35].…”

Section: Introductionmentioning

confidence: 98%

On the existence and regularity of solutions of semi-hyperbolic patches to 2-D Euler equations with van der Waals gas

Barthwal,

Sekhar

2021

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This article is concerned in establishing the existence and regularity of solution of semi-hyperbolic patch problem for two-dimensional isentropic Euler equations with van der Waals gas. This type of solution appears in the transonic flow over an airfoil and Guderley reflection and is very common in the numerical solution of Riemann problems. We use the idea of characteristic decomposition and bootstrap method to prove the existence of global smooth solution which is uniformly C 1, 1 2 continuous up to the sonic curve. We also prove that the sonic curve is C 1, 1 2 continuous. Further, we show the formation of shock as an envelope for positive characteristics before reaching their sonic points.

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