Compression fans for mixed-type dark energy supersonic flow past a concave corner and concave bend

Hanxuan Wang; Lihui Guo; Hanxuan Wang; Lihui Guo

doi:10.3934/math.20261197

AIMS Mathematics

2026, Volume 11, Issue 9: 30214-30232. doi: 10.3934/math.20261197

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Research article

Compression fans for mixed-type dark energy supersonic flow past a concave corner and concave bend

Hanxuan Wang ,
Lihui Guo ^,

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

Received: 30 June 2026 Revised: 08 September 2026 Accepted: 09 September 2026 Published: 16 September 2026
MSC : 35L53, 58J32, 58J45, 76J20

This paper mainly considers the problem of the supersonic horizontal upstream flow of mixed-type dark energy fluid turning a concave corner and a concave bend. We obtain explicit expression of the global solutions, which contain compression fans. The results differ from the structure of oblique shock wave solutions for polytropic gas. These are caused by the nonconvexity of mixed-type dark energy fluid.
- Euler equations,
- the mixed-type dark energy fluid,
- concave corner,
- concave bend,
- compression fans
Citation: Hanxuan Wang, Lihui Guo. Compression fans for mixed-type dark energy supersonic flow past a concave corner and concave bend[J]. AIMS Mathematics, 2026, 11(9): 30214-30232. doi: 10.3934/math.20261197

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Abstract

This paper mainly considers the problem of the supersonic horizontal upstream flow of mixed-type dark energy fluid turning a concave corner and a concave bend. We obtain explicit expression of the global solutions, which contain compression fans. The results differ from the structure of oblique shock wave solutions for polytropic gas. These are caused by the nonconvexity of mixed-type dark energy fluid.

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