Noble-Abel gas diffusion at convex corners of the two-dimensional compressible magnetohydrodynamic system

Fei Zhu; Fei Zhu

doi:10.3934/math.20241156

AIMS Mathematics

2024, Volume 9, Issue 9: 23786-23811. doi: 10.3934/math.20241156

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Research article

Noble-Abel gas diffusion at convex corners of the two-dimensional compressible magnetohydrodynamic system

Fei Zhu ^,

College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830017, China

Received: 11 June 2024 Revised: 30 July 2024 Accepted: 05 August 2024 Published: 09 August 2024
MSC : 35A01, 76N25

In this paper, we study the expansion of Noble-Abel gas into a vacuum around the convex corner of the two-dimensional compressible magnetohydrodynamic system. We reduce this problem to the interaction of a centered simple wave emanating from the convex corner with a backward planar simple wave. Mathematically, this is a Goursat problem. By using the method of characteristic decomposition and construction of invariant regions, combining $ C^{0} $ and $ C^{1} $ estimation as well as hyperbolicity estimation, we obtain the existence of a global classical solution by extending the local classical solution.
- gas diffusion,
- convex corner,
- compressible magnetohydrodynamic system,
- Noble-Able gas,
- goursat problem
Citation: Fei Zhu. Noble-Abel gas diffusion at convex corners of the two-dimensional compressible magnetohydrodynamic system[J]. AIMS Mathematics, 2024, 9(9): 23786-23811. doi: 10.3934/math.20241156

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Abstract

In this paper, we study the expansion of Noble-Abel gas into a vacuum around the convex corner of the two-dimensional compressible magnetohydrodynamic system. We reduce this problem to the interaction of a centered simple wave emanating from the convex corner with a backward planar simple wave. Mathematically, this is a Goursat problem. By using the method of characteristic decomposition and construction of invariant regions, combining $ C^{0} $ and $ C^{1} $ estimation as well as hyperbolicity estimation, we obtain the existence of a global classical solution by extending the local classical solution.

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