$$L^{1}$$ convergences and convergence rates of approximate solutions for compressible Euler equations near vacuum

Lee, Hsin Yi; Chu, Jay; Hong, Ji; Lin, Yow−Jon

doi:10.1007/s40687-020-00205-8

Cited by 2 publications

(3 citation statements)

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“…We also observe that the solutions seem to be convergent as ν tends to 0. This coincides with the results in [14]. In the second numerical experiment, we consider the case apxq " e 1´p1{xq , i.e., kpxq " 1{x 2 .…”

Section: Numerical Experimentssupporting

confidence: 84%

“…These results were extended to some related systems by Chen, Young, and Zhang [5], such as MHD equations and compressible Euler equations for the fluid in variable area ducts. To the subject of fluid near vacuum (or containing vacuum), we refer the readers to [2,14,21,22]. To the weak solutions of hyperbolic conservation laws, we refer the readers to [6,8,10,14,20,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

“…To the subject of fluid near vacuum (or containing vacuum), we refer the readers to [2,14,21,22]. To the weak solutions of hyperbolic conservation laws, we refer the readers to [6,8,10,14,20,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

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Global Classical Solutions Near Vacuum to the Initial-Boundary Value Problem of Isentropic Supersonic Flows through Divergent Ducts

Lin¹,

Chu²,

Hong³

et al. 2022

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In this paper, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem modeling isentropic supersonic flows through divergent ducts. The governing equations are the compressible Euler equations with a small parameter, which can be written as a hyperbolic system in terms of the Riemann invariants with a non-dissipative source. We provide a new result for the global existence of classical solutions to initial-boundary value problems of non-dissipative hyperbolic balance laws without the assumption of small data. The work is based on the local existence, the maximum principle, and the uniform a priori estimates obtained by the generalized Lax transformations. The asymptotic behavior of classical solutions is also shown by studying the behavior of Riemann invariants along each characteristic curve and vertical line. The results can be applied to the spherically symmetric solutions to N -dimensional compressible Euler equations. Numerical simulations are provided to support our theoretical results.

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Section: Numerical Experimentssupporting

confidence: 84%