The relaxation limit of a compressible gas-liquid model with well-reservoir interaction. (English) Zbl 1513.76151
Summary: In this paper, we are concerned with the motion of gas-kick flow in oil wells for the extreme case where the pressure is largely dictated by the surrounding reservoir pressure. Formally, the model can be obtained by taking the relaxation limit of a two-phase compressible gas-liquid model with a pressure-dependent well-reservoir interaction term. Under suitable smallness assumptions upon the initial data, the global existence as well as the uniqueness of strong solutions to the model is investigated by using the energy method. Besides, the large-time behavior of the solution is also studied. Our results generalize the ones in [S. Solem and S. Evje, Z. Angew. Math. Phys. 68, No. 1, Paper No. 23, 25 p. (2017; Zbl 1431.76132)].
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
Citations:
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| [27] | P. R. China E-MAIL: gyhmath05@outlook.com HONGYUN PENG: School of Applied Mathematics Guangdong University of Technology Guangzhou, 510006, P. R. China E-MAIL: penghy010@163.com CHANGJIANG ZHU (corresponding author): School of Mathematics South China University of Technology Guangzhou, 510641, P. R. China E-MAIL: machjzhu@scut.edu.cn KEY WORDS AND PHRASES: Two-phase flow, well-reservoir flow, relaxation limit, large-time behav-ior. · Zbl 1195.35245 · doi:10.1007/s00220-009-0914-1 |
| [28] | MATHEMATICS SUBJECT CLASSIFICATION: 76T10, 76N10, 35B40, 35Q35. Received: March 23, 2020. |
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